diff --git "a/ENE3T4oBgHgl3EQfVQoB/content/tmp_files/load_file.txt" "b/ENE3T4oBgHgl3EQfVQoB/content/tmp_files/load_file.txt" new file mode 100644--- /dev/null +++ "b/ENE3T4oBgHgl3EQfVQoB/content/tmp_files/load_file.txt" @@ -0,0 +1,1513 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf,len=1512 +page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='04457v1 [gr-qc] 11 Jan 2023 Ghost and Laplacian Instabilities in Teleparallel Horndeski Gravity Salvatore Capozziello,1, 2, 3, ∗ Maria Caruana,4, 5, † Jackson Levi Said,4, 5, ‡ and Joseph Sultana6, § 1Dipartimento di Fisica ”E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Pancini”, Universit`a degli Studi di Napoli, ”Federico II”, Complesso Universitario Monte S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Angelo, Via Cinthia 9 Edificio G, 80126 Napoli, Italy 2Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Napoli Complesso Universitario Monte S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Angelo, Via Cinthia 9 Edificio G, 80126 Napoli, Italy 3Scuola Superiore Meridionale, Largo San Marcellino 10, 80138 Napoli, Italy 4Institute of Space Sciences and Astronomy, University of Malta, Msida, Malta 5Department of Physics, University of Malta, Msida, Malta 6Department of Mathematics, University of Malta, Msida, Malta Teleparallel geometry offers a platform on which to build up theories of gravity where torsion rather than curvature mediates gravitational interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The teleparallel analogue of Horndeski gravity is an approach to teleparallel geometry where scalar-tensor theories are considered in this torsional framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Being teleparallel gravity of lower order in dynamics, this turns out to be more general than metric Horndeski gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' In other words, the class of teleparallel Horndeski gravity models is much broader than the standard metric one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' In this work, we explore constraints on this wide range of models coming from ghost and Laplacian instabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The aim is to limit pathological branches of the theory by fundamental considerations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' It is possible to conclude that a very large class of models results physically viable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' INTRODUCTION General relativity (GR) has been the gravitational foundation of cosmology for over a century.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Its latest embodiment appears in a picture wherein the evolutionary processes of the Universe are described in the framework of the so-called ΛCDM model [1, 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Supported by overwhelming observational evidences, this model describes a Universe started with a big bang, then driven through an inflationary phase and other well known epochs to eventually produce an accelerating Universe at late-times [3, 4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' In the ΛCDM model, the late time acceleration expansion is driven by the cosmological constant or some form of dark energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Despite a lot of foundational works, internal consistency issues persist in this respect [5–7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Recently, observational challenges to the standard model has arisen in the form of cosmological tensions with statistically significant differences between predictions of expansion from early time data [8–10] and measurements from late time [11, 12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' These tensions continue to increase with new survey data [13–15], and may permeate into other sectors of cosmology besides expansion [16–18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' This situation leads to take into account potential alternatives to the standard cosmological ΛCDM model in the context of possible modifications to the gravitational sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' A solution to the problem of cosmic tensions, as well as of other longstanding issues, can be offered by alternative theories of gravity, in particular by scalar-tensor gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Scalar fields improve GR in view of Mach principle and could naturally address several issues in cosmology and astrophysics like inflation, dark matter and dark energy [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The most general scalar-tensor theory of gravity, where scalar fields are minimally and non-minimally coupled to curvature, is the so-called Horndeski gravity [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' It is the most general theory of gravity producing second order field equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' This is advantageous because nature appears to produce, generally, second order equations of motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Furthermore, higher order theories can produce Ostrogradsky instabilities making second order theories more attractive from a fundamental perspective [21–23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Horndeski gravity is formulated by four free functions of the scalar field and its kinetic term [24, 25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' This offers a rich phenomenology on which to produce dark energy models but also dark matter and inflation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' However, recent multimessenger observations by the LIGO collaboration, in the gravitational event GW170817 [26], and measurements of the companion electromagnetic counterpart, namely GRB170817A [27], has placed stringent constraints on the speed of propagation of gravitational waves (GW) to within deviations of at most one part ∗ capozziello@na.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='infn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='it † maria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='caruana.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='16@um.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='mt ‡ jackson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='said@um.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='mt § joseph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='sultana@um.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='mt 2 in 1015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Considering these constraints, many branches of Horndeski gravity have been disqualified in regular curvature-based gravity [28–30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' However, Horndeski gravity has a number of interesting generalizations [31] where higher order terms, avoiding the Ostrogradsky instabilities, can be incorporated into the theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Another possibility is to reconsider the geometric foundations of curvature on which Horndeski gravity is built.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Curvature can be expressed through the Levi-Civita connection Γ λ µν obtained from the metric [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Here an over-circle represents quantities determined by the Levi-Civita connection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' In teleparallel gravity (TG), the teleparallel connection (Γλ µν) replaces the Levi-Civita connection and so dynamics of gravity is replaced from curvature to torsion [32–35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The teleparallel connection is curvatureless and satisfies metricity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' For this reason, the teleparallel Ricci scalar turns out to identically vanish, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' R = 0 (this is not to say that the standard Ricci scalar is zero, being, in general, R ̸= 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' On the other hand, TG naturally produces a torsion scalar (T ) [33], which turns out to be equal to the curvature-based Ricci scalar up to a boundary term (B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' For this reason, the linear torsion scalar produces the Teleparallel equivalent of General Relativity (TEGR) which is dynamically equivalent to GR in the classical regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' This distinction between the torsion scalar, producing second order terms in the equations of motion, and the boundary term, producing fourth order terms in the equations of motion (when the boundary term is nonlinear in the action), gives rise to a much richer landscape of theories on which to build cosmological models, if compared with the standard Einstein-Hilbert action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Another way to conceptualize this feature is through the teleparallel analogue of the Lovelock theorem [36–38] which produces a much wider range of actions with second order field equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Equivalences and differences of these representations are discussed in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Similar to GR, TEGR features many modifications such as f(T ) gravity [34, 40–46] which is generically second order in nature, as well as f(T, B) gravity [47–55] which now features fourth order contributions similar to f( R) gravity [19, 56–62].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' There have also been various formulations of scalar–tensor gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' See, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [63–65].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Equipped with the TG formalism, one can consider the teleparallel analogue of Horndeski gravity [38] where the generically lower order nature of TG turns out to produce a much richer structure to be developed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' This feature directly comes from the teleparallel analogue of the Lovelock theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' This larger framework of models means that there are many more classes of theories that now satisfy the speed of GWs constraint [66, 67] as required from the above mentioned multimessenger analysis [68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' This class of gravitational models also satisfies the parameterized post-Newtonian observational constraints [69] for a large number of models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The teleparallel analogue of Horndeski gravity also produces a number of interesting cosmologies such as those which are well-tempered [70, 71], as well as those that are derived from Noether symmetry considerations [72–76].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' In this way, all models that were previously disqualified in regular Horndeski may be revived in this new formalism based on TG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' In this work, we perform a stability analysis of the teleparallel analogue of Horndeski gravity through considerations on a Minkowski spacetime background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The Minkowski background is an ideal arena to probe the fundamental behavior of theories with large classes of models since any astrophysical or cosmological setting must first be stable on a Minkowski spacetime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' In our analysis, we consider both background and leading order perturbations in the context of a scalar-vector-tensor decomposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' This is important to fully decompose any potentially problematic part of the theory in detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' In the TG setting, this is more intricate since the metric tensor (gµν) is replaced as the fundamental dynamical variable of the field equations with the tetrad (eA µ) and the spin connection (ωA Bµ), which are discussed in detail later on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' In all cases, we focus our study on the ghost and gradient instabilities, which can wreak havoc on gravitational models since this may, respectively, produce scalar field kinetic terms with the wrong sign and unbounded propagation speeds of particular perturbations, which can lead to unphysical models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The structure of the manuscript is the following: in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' II, we summarize TG and its teleparallel analogue of Horndeski gravity;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' this then leads to the Minkowski background equations of motion in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Scalar– vector–tensor perturbations are discussed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' From these perturbations, we are able to explore potential instabilities in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' V where our main results are reported.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Discussion and conclusions are drawn in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' In this work, we use geometric units and the signature (−, +, +, +).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 3 II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' TELEPARALLEL HORNDESKI GRAVITY GR, a curvature-based theory, is constructed on torsionless Levi-Civita connection Γλ µν, where, as said above, the overhead circle (◦) represents quantities built with this connection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' This leads to numerous theories of gravity beyond GR as the gravitational field can be expressed through the Riemann tensor and its contractions such as the Ricci tensor and the Riemann scalar [59], the latter produces the Einstein- Hilbert action [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' On the other hand, TG incorporates the teleparallel connection, dubbed as teleparallel connection Γλ µν, leading to a theory satisfying the curvature-less and metricity conditions [32–35], resulting in a torsionful theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Later in this section, it will be shown that even though the Ricci scalar R vanishes, due to the symmetry of the connection, the curvature-ful connection gives a non-zero value for the Riemann tensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Hence, the Ricci scalar R can be defined through teleparallel quantities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The fundamental dynamical object of GR is the metric tensor gµν, but within TG, the metric is expressed through the tetrad eA µ, which acts as a transformation between the local and general manifold spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The tetrad and the inertial spin connection ωB Cν become the fundamental objects [33] while creating a link between the general manifold denoted through Greek indices to the local Minkowski manifold denoted by Latin indices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Thus, the relationship between Minkowski and general spacetimes is given by [77] gµν = ηAB eA µ eB ν , ηAB = gµν E µ A E ν B , (1) where E µ A is the inverse tetrad which satisfies orthogonality conditions eA µ E µ B = δA B , eA µ E ν A = δν µ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (2) The teleparallel connection is defined through the TG variables as [34, 35] Γλ µν = E λ A � ∂νeA µ + ωA BνeB µ � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (3) Note, the quantities without an overhead circle will correspond to those objects that are related to teleparallel gravity or calculated on its connection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The condition ∂[µωA |B|ν] + ωA C[µωC |B|ν] ≡ 0 , (4) results in a flat spin connection [32], where square brackets denote the antisymmetric operator, and can equivalently be used to determine the components of the spin connection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The local Lorentz transformation (LLT), wherein ΛA B represents Lorentz boosts and rotations, is used to define the spin connection ωA Bµ = ΛA C ∂µΛ C B [33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' It plays a role in the ��eld equations since an infinite number of tetrad choices could satisfy Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (1) for a particular metric, thus the spin connection is used to counterbalance inertial effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' This ensures the theory, in this case TG, remains covariant [78].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Moreover, there exists a Lorentz frame such that the spin connection is set to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' It is referred to as the Weitzenb¨ock gauge [35, 79].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Hence, from this point onwards, the spin connection will be dropped following the application of the aforementioned gauge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Similar to how the Riemann tensor, constructed on the Levi-Civita connection, is associated to the cur- vature property of GR, the analogy of this for TG is the torsion tensor defined by the teleparallel connec- tion [35, 80] T A µν = ΓA νµ − ΓA µν .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (5) While curvature in GR is defined as a deformation of spacetime, the torsion tensor in TG represents the field strength of gravitation that transforms covariantly under LLTs and diffeomorphisms [78].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Another important aspect of TG is that the torsion tensor can be decomposed in irreducible parts [81–83], namely aµ = 1 6ǫµνλρ T νλρ , (6) vµ = T λ λν , (7) tλµν = 1 2(Tλµν + Tµλν) + 1 6(gνλvµ + gνµvλ) − 1 3gλµvν , (8) 4 giving the axial, vectorial and tensorial pieces, respectively, and ǫABCD being the four-dimensional Levi- Civita tensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Hence, the respective scalar invariants are given by [47, 82] Tax = aµaµ = − 1 18Tλµν(T λµν − 2T µλν) , (9) Tvec = vµvµ = T λ λµT ρµ ρ , (10) Tten = tλµνtλµν = 1 2Tλµν(T λµν + T µλν) − 1 2T λ λµT ρµ ρ , (11) which, under parity transformation, are invariant scalars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' On the other hand, terms such as P1 = vµaµ and P2 = ǫµνσρtλµνtλ ρσ are excluded due to parity-violation [38, 81].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The combination of the scalar invariants leads to the torsion scalar T = 3 2Tax + 2 3Tten − 2 3Tvec = 1 2 � E λ A gρµE ν B − 2E ρ B gλµE ν A + 1 2ηABgµρgνλ � T A µνT B ρλ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (12) An identical result can be obtained through contraction between the torsion tensor and the superpotential S µν A which represents the potential relation of the gravitational energy-momentum tensor [80, 84, 85]: S µν A = 1 2 � Kµν A − E ν A T αµ α + E µ A T αν α � , (13) where Kλ µν = Γλ µν − Γλ µν = 1 2 � T λ µ ν + T λ ν µ − T λ µν � (14) is the contorsion tensor relating TG and GR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' These quantities can be used to form the torsion scalar [34], written as T = S µν A T A µν , (15) which can be shown to be equivalent to the result obtained in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The Ricci scalar dependent on the teleparallel connection, which vanishes, can be related, using the contorsion tensor, to the regular Ricci scalar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' This results in a relationship between the Levi-Civita and the teleparallel connections defined Ricci scalar [47, 77] R = R + T − B = 0 , (16) where B = 2 e∂µ(e T λ µ λ ) = 2 ∇µT λ µ λ is a boundary term and e = det(eA µ) = √−g is the tetrad determinant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Hence, the curvature-ful Ricci scalar is non-vanishing being R = −T + B .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (17) The total divergence term found in B accounts for the fourth order derivative contributions to the field equations in modified theories of gravity [47, 54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' This is embodied within the Ricci scalar in GR [57, 59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Thus, the Teleparallel Equivalent of General Relativity (TEGR) [86, 87] is defined as the linear appearance of the torsion scalar since both Lagrangians are equal up to a boundary term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The equivalence principle in GR allows one to raise local Lorentz frames from a Minkowski metric to a general metric tensor, and additionally, partial derivatives are raised to covariant derivatives defined by the Levi-Civita connection [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' This procedure, referred to as the minimal coupling prescription, if applied within TG, is preserved for additional fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Minkowski tetrads are raised to arbitrary ones and tangent space partial derivatives are exchanged for covariant derivatives based on Levi-Civita connection [33, 88] ∂µ → ∇µ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (18) Thus, by having both gravitational and scalar fields well developed, it is possible to look at the teleparallel analogue of Horndeski gravity, referred to at times as Bahamonde-Dialektopoulos-Levi Said (BDLS) the- ory [38, 66, 69].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The construction of BDLS theory depends on the following criteria: (1) field equations are 5 at most second order with respect to the tetrad and scalar;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (2) as previously mentioned, scalar invariants do not violate parity;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (3) contractions of the torsion tensor are at most quadratic [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' All of these requirements allow for an adequate extension of the standard metric Horndeski gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Note that Lovelock’s theorem states that Einstein fields equations are the only second-order field equations from a Lagrangian density constructed through a four-dimensional metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' TG allows for the weakening of Lovelock [36, 37] theory as an additional scalar field φ is introduced, giving rise to further terms in the gravitational action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Starting off with the non-minimal coupling of scalar and torsion field, the linear contraction is given by [38] I2 = vµ ◦∇µφ , (19) being the scalar I1 = tλµν ∇λφ ∇µφ ∇µφ = 0, due to the complete symmetry of the tensor decomposition, Furthermore I3 = aλ ∇λφ violates the parity condition due to an odd number of axial parts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Moreover,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' the quadratic contractions of this nature are given by [38] J1 = aµaν ◦∇µφ ∇νφ ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (20) J3 = vλtλµν ◦∇µφ ∇νφ ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (21) J5 = tλµνt α λ ν ∇µφ ∇αφ ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (22) J6 = tλµνt αβ λ ∇µφ ∇νφ ∇αφ ∇βφ ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (23) J8 = tλµνt α λµ ∇νφ ∇αφ ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (24) J10 = ǫµ νλρaνtαρλ ◦∇µφ ∇αφ ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (25) while other possibilities are eliminated as they have already been included: J2 = vµvν ◦∇µφ ∇νφ = I2 2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' J4 = vµtλµν ◦∇λφ ∇νφ = J3 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' J7 = tλµνtαβ λ ∇µφ ∇νφ ∇αφ ∇βφ = −2J6 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (26) while J9 = tλµνtαβγ ∇λφ ∇µφ ∇νφ ∇αφ ∇βφ ∇γφ = 0 due to the total symmetry of the tensor irreducible part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Hence, BDLS action is described by [38] SBDLS = 1 2κ2 � d4x e LTele + 1 2κ2 5 � i=2 � d4x e Li + � d4x e Lm , (27) where LTele = GTele(φ, X, T, Tax, Tvec, I2, J1, J3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='J5, J6, J8, J10) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (28) Here GTele is an arbitrary function, X := − 1 2∂µφ∂µφ and L2 := G2(φ, X) , (29) L3 := −G3(φ, X) □φ , (30) L4 := G4(φ, X)(−T + B) + G4,X(φ, X)[( □φ)2 − ∇µ ∇νφ ∇µ ◦∇νφ] , (31) L5 := G5(φ, X) Gµν ∇µ ∇νφ − 1 6G5,X(φ, X)[( □φ)3 + 2 ∇µ ∇νφ ∇ν ∇αφ ∇α ∇µφ − 3 ∇µ ∇νφ ∇µ ◦∇νφ □φ] , (32) which are identical to the standard metric Horndeski Lagrangians [20] but calculated using the tetrad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Finally, Lm is the matter Lagrangian in Jordan conformal frame, Gµν is the Einstein tensor, and κ2 = 8πG where G is the gravitational constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' MINKOWSKI BACKGROUND EQUATIONS IN TELEPARALLEL HORNDESKI GRAVITY Let us explore now perturbations on a Minkowski background within the gravitational theory of teleparallel analogue of Horndeski.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Firstly, we tackle the background equations for a general flat Friedman–Lemaˆıtre–Robertson–Walker 6 (FLRW) metric to obtain the necessary constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Then, this is followed by the analysis for perturbation theory up to second order which is needed for our approach since we consider the Euler-Lagrange equations to get the cosmological equations of motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The flat FLRW metric in Cartesian coordinates is given by ds2 = −N(t)2dt2 + a(t)2(dx2 + dy2 + dx2) , (33) where N(t) is the lapse function and a(t) is the scale factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' As previously mentioned, this follows the metric signature that is mostly positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The tetrad can be written in diagonal form as [35] eA µ = diag(N(t), a(t), a(t), a(t)) , (34) which is compatible with the Weitzenb¨ock gauge giving a vanishing spin connection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Hence, the action in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (27) can be re-expressed in terms of these background quantities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Friedman equations are then obtained by varying with respect to the lapse function and scale factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Additionally, the scalar field Klein-Gordon equation can be obtained by varying with respect to the scalar field [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Since we will be working in Minkowski background, the limits N(t) → 1 and a(t) → 1 are taken.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Hence,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' the constraints obtained from the Friedman equation and scalar field variation in Minkowski background are given by 0 = −G2 − GTele + 2XG2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='X − 2XG3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='φ + 2XGTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='X ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (35) 0 = G2 + GTele − 2XG3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='φ + 4XG4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='φφ + 2¨φG4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='φ − 2X ¨φG3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='X + 4X ¨φG4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='φX − d dt( ˙φGTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='I2) ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (36) 0 = G2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='φ + GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='φ − 2XG2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='φX + 2XG3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='φφ − 2XGTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='φX − G2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='X ¨φ + 2G3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='φ ¨φ − GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='X ¨φ − 2X ¨φGTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='X − 2X ¨φG2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='XX + 2X ¨φG3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='φX − 2X ¨φGTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='XX ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (37) where all scalar invariants are background quantities and comma ( ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' ) denotes partial derivative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Moreover, the scalar field equation can also be expressed in terms of a Klein-Gordon equation as shown in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' SECOND ORDER PERTURBED ACTION WITH SCALAR-VECTOR-TENSOR DECOMPOSITION Here, we calculate the perturbed action up to second order terms which are necessary for the Euler- Lagrange method to find the equations of motion of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' By taking perturbations about a Minkowski background for both tetrad and scalar field, we can build the action up to second order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The tetrad and scalar perturbation are respectively given by eA µ → eA µ + ǫ δeA µ = δA µ + ǫ δeA µ , (38) φ → φ + ǫ δφ , (39) where ǫ is the perturbation parameter representing the perturbation order of background Minkowski tetrad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' It is given by a four-dimensional identity matrix given by the Kronecker delta δA µ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' It is sufficient to expand the scalar field up to first order since higher order terms do not contribute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Additionally, it should be noted that the background scalar field can be taken to be as a function of time and apply the unitary gauge such that φ → φ(t) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (40) Moreover,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' the perturbations of arbitrary functions present in the Lagrangian are obtained by performing a Taylor expansion up to second order such that Gi(φ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' X) = Gi + ǫ Gi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='XX(1) + ǫ2 � 1 2Gi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='XX(X(1))2 + Gi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='XX(2)� ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (41) GTele(φ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' X,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Tax,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Tvec,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' I2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' J1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' J3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' J5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' J6,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' J8,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' J10) = GTele + ǫ(GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='XX(1) + GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='I2I(1) 2 ) + 1 2ǫ2(GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='XX(X(1))2 + GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='I2I2(I(1) 2 )2) + ǫ2� GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='XX(2) + GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='T T + GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='TaxTax + GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='TvecTvec + GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='I2I(2) 2 � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (42) 7 where,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' for i = {2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 5},' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' j = {X,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' XX} and k = {X,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Tax,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Tvec,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' XX,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' I2I2},' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Gi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='j and GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='k are background functions,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' such that XX and I2I2 are the second order derivatives with respect to X and I2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The numbered superscripts represent the order of perturbation of the scalar invariant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' In this section, we consider a scalar-vector-tensor (SVT) decomposition of the tetrad based on the formal- ism applied in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [89] for first order perturbations: δeA µ := \uf8ee \uf8f0 ϕ −(∂iβ + βi) δI i (∂ib + bi) δIi � −ψδij + ∂i∂jh + ∂ihj + ∂jhi + 1 2hij + ǫijk(∂kσ + σk) � \uf8f9 \uf8fb , (43) where {ϕ, β, b, ψ, h} are scalars and σ is a pseudoscalar of 1 degree of freedom (DoF) each, {βi, bi, hi} are vectors and σi is a pseudovector of 1 DoFs each, and hij is the tensor mode of 2 DoFs, for a total of of 16 DoFs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The tensor modes are symmetric hij = h(ij), traceless δijhij = 0 and divergenceless ∂ihij = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' See also Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [90, 91].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The divergenceless property also applies for vectors and pseudovectors such that ∂iαi = 0 where α = {β, b, h, σ}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Unlike Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [92, 93], the pseudoscalar and pseudovector are included to account for the anti-symmetry of the tetrad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The mid-range Latin indices are spacial coordinates: {I, J, K, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='} for spacial inner bundle and {i, j, k, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='} for spacial spacetime manifold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Note, δij is the spacial Minkowski metric such that δij = −ηij.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' In turn, the first order metric perturbation from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (1) is given by δgµν = \uf8ee \uf8f0 2ϕ ∂iB + Bi ∂iB + Bi 2 � −ψδij + ∂i∂jh + ∂ihj + ∂jhi + 1 2hij � \uf8f9 \uf8fb , (44) where B = −β + b and Bi = −βi + bi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The off-diagonals are identical hence verifying the symmetry of the metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The pseudoscalar and pseudovectors no longer play a role, and thus, the number of DoFs reduces to 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The gauge transformation through the coordinate change [94–96] is ˜xµ → xµ + ξµ , (45) where ξµ is a vector field applied to study the gauge transformation of perturbative quantities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Such a coordinate transformation can be extended to include orders higher than second one, but it is sufficient to consider up to this point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Thus, the transformations for first tetrad are given by [97] δ˜eA µ = δeA µ + Lξ(1)eA (0) µ , (46) where Lξ is the Lie derivative along ξµ wherein ξµ = (ξ0, ξi + δij∂jξ) further splits and once again obeys divergencelessness as ∂iξi = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The analysis of each combination of temporal and spatial parts of the tetrad indicates that ψ, σ, βi and hij are gauge invariant in Minkowski background while the rest have the following gauge transformations ˜ϕ = ϕ − ˙ξ0 , β = β − ξ0 , ˜b = b − ˙ξ , ˜h = h − ξ , ˜bi = bi + ˙ξi , ˜hi = hi + 1 2ξi , ˜σi = σi − 1 2ǫijk∂jξk .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (47) This shows that since the pseudoscalar σ is gauge-invariant, it can be treated separately than the rest of the scalar modes, but the same cannot be said for the pseudovector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' In fact, the pseudovector σi can be expressed in terms of hi (and its derivative in terms of bi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' This implies that the vector and pseudovector cannot be decomposed [98].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Next, we construct groups of non-gauge invariant quantities: {ϕ, β}, {b, h} and {bi, hi, σi}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' For gauge choice, a quantity from each group is set to zero [98].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' In particular, we will choose β = 0, h = 0 and σi = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' GHOST AND LAPLACIAN INSTABILITIES IN MINKOWSKI BACKGROUND Ghost instabilities stem from a negative kinetic term in the action associated to a propagating degree of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' A ghost mode can be determined by expanding the action up to second order perturbations about 8 a background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Therefore, for a Lagrangian of the form L = ˙⃗χtA ˙⃗χ + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=', we impose that the eigenvalues of A should be positive to eliminate ghost modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The procedure is applied in what follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The second order perturbation of the action is obtained by separately applying the scalar, vector and tensor field perturbations given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (43).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The dynamical fields in the action are identified, while a system of equations is obtained by varying the action with respect to the auxiliary fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' This system of equations is substituted back into the action to eliminate the non-dynamic fields [99, 100].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' In order to obtain a gauge invariant action, the action is varied with respect to the temporal and spatial part of the vector field associated with the coordinate transformation, and imposing that this vanishes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Then, a diagonalized kinetic matrix is constructed and a constraint is generated for each entry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' In general, these constraints could be time dependent: this feature arises from the background spacetime and the background quantities of fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' When looking at the propagating speeds of these modes, a positive definite value should be applied in order to ensure that the perturbation does not lead to an exponential growth [101] i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' c2 > 0, referred to as gradient or Laplacian instability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Hence, both ghost and gradient instabilities are checked for each mode in order to obtain the constraints which lead to a stable model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Tensor Perturbations The tensor mode perturbations, presented in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (43), can be extended as eA µ → \uf8ee \uf8f01 0 0 δij + 1 2ǫhij − 1 8ǫ2hikhk j \uf8f9 \uf8fb , (48) analogous to the Arnowitt-Deser-Misner (ADM) for tensor modes [100].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The action can be extended to second order perturbations such that S(2) T = 1 2 � d4x � MT ˙hij ˙hij − NT ∂mhij∂mhij + Phijhij� (49) where MT = G4 − 2XG4,X + XG5,φ − GTele,T + 1 2XGTele,J5 + 2XGTele,J8 , (50) NT = G4 − X(G5,φ + ¨φG5,X) − GTele,T , (51) PT = − 1 2 d dt( ˙φGTele,I2) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (52) For the sake of simplicity, we switch to Fourier space such that S(2) T = 1 2 � dt d3k (2π)3 � MT ˙hij ˙hij + � −k2NT + PT � hijhij .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' � (53) This result is obtained after applying integration by parts, removing the surface terms and applying the background Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (35-37).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' By imposing MT > 0, the theory is ghost free in tensor modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' When considering a constant background scalar φ, this implies that G4 − GTele,T > 0 which corresponds to the condition G4 −GTele,T ̸= 0 imposed in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [102] in order to ensure that there are tensor mode DoFs propagating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The propagation speed of tensor modes is given by c2 T = NT MT = G4 − X(G5,φ + ¨φG5,X) − GTele,T G4 − 2XG4,X + XG5,φ − GTele,T + 1 2XGTele,J5 + 2XGTele,J8 , (54) for which c2 T > 0 is required to ensure gradient stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Hence, MT > 0 and NT > 0 result in ghost and gradient stability, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The same result would by obtained when eliminating I2 contribution from the GTele function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Following the observations of gravitational wave signal GW170817 [103] and its electromagnetic counterpart GRB170817A [27],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' it is interesting to calculate the deviation from speed of light propagation such that the excess speed is given by αT = c2 T − 1 = X(2G4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='X − 2G5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='φ − ¨φG5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='X − 1 2GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='J5 − 2GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='J8) G4 − 2XG4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='X + XG5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='φ − GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='T + 1 2XGTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='J5 + 2XGTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='J8 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (55) 9 which corresponds to the result obtained through the GW propagation equation [66],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' a value which is highly constrained such that a graviton mass would be minute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Additionally, from the general result of teleparallel Horndeski analogue, given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (48), one may obtain the results of well-studied theories from literature, as summarized in Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' See also Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [73] for the metric cases derived from Noether symmetries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' As an extension analogous to standard Horndeski theory, the stability conditions can be obtained by setting GTele = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The ghost modes are excluded for when the constant of the kinetic term is G4 − 2XG4,X + XG5,X > 0 while gradient stability is obtained for G4 − X(G5,φ + ¨φG5,X) > 0, in agreement with Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [101, 104–106] when taking the appropriate limits to Minkowski spacetime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' An example of a subclass of Horndeski gravity is the Brans-Dicke theory, where G2 = 2wBDX φ and G4 = φ for which wBD is the Dicke coupling constant [107], other constants are set to vanish and ghost instabilities are avoided for φ > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' By considering the generalized Brans Dicke theory, ghost instabilities are avoided for a positive value of a function of the scalar field, F(φ) > 0 [108].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Another example is f( R) where G2 = f(φ) − φf ′(φ), G4 = f ′(φ), the rest of the constants are zero, implying that ghost stability is achieved for f ′(φ) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' A final subcase of Horndeski gravity considered here is GR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' In this case, the only non-vanishing constant is G4 = 1 for which there are no ghost modes since MT = 1 > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' All of these subcases do not result in any gradient instabilities as cT = 1 > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Next, we look at cases that arise due to the inclusion of teleparallel terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' For a purely teleparallel theory such as f(T ) gravity, all terms are set to vanish except for GTele,T = f(T ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' This implies in −f ′(T ) > 0 to avoid ghost modes similar to the result obtained in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [98].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' An equivalent result is obtained for scalar- tensor theory with a Lagrangian of the form L = f(φ, T ) + XP(φ), an extension of f(T ) [100, 109].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Once again, gradient instabilities are not an issue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Finally, the case where only I2 contributions are present is considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' In this case, all constants are going to vanish while GTele,I2 ̸= 0 leads to a non-dynamical degree of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Theory Case MT NT Horndeski GTele = 0 G4 − 2XG4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='X + ¨φXG5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='X G4 − X(G5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='φ + ¨φG5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='X) Generalized Brans-Dicke GTele = G5 = 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' G2 = B(φ)X G3 = 2ξ(φ)X,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' G4 = 1 2F(φ) 1 2F(φ) 1 2F(φ) Brans-Dicke GTele = G3 = G5 = 0 G2 = 2wBDX φ ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' G4 = φ φ φ f( R) GTele = G3 = G5 = 0 G2 = f(φ) − φf ′(φ),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' G4 = f ′(φ) f ′(φ) f ′(φ) General Relativity GTele = G2 = G3 = G5 = 0 G4 = 1 1 1 Teleparallel or f(T ) G2 = G3 = G4 = G5 = 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' GTele = f(T ) −f ′(T ) −f ′(T ) f(φ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' T ) + XP(φ) G3 = G4 = G5 = 0 G2 = XP(φ),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' GTele = f(φ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' T ) −f,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='T (φ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' T ) −f,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='T (φ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' T ) GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='I2 only G2 = G3 = G4 = G5 = 0 GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='T = 0 no propagating mode TABLE I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' List of literature models with the respective ghost MT and gradient stability NT conditions are positive definite, while the propagation speed is cT = NT/MT for tensor modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The models include Horndeski theory [20, 101, 104, 105], Generalized Brans-Dicke [108] and Brans-Dicke [107], f(˚ R) theory, General Relativity, f(T ) theory [98], f(φ, T ) theory [100] and the case where the action is dependent on I2 only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 10 B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Vector Perturbations Next, we consider the vector perturbation of the tetrad (43) with the application of gauge fixing which eliminates the pseudovector and any coupling with it such that eA µ → \uf8ee \uf8f0 1 −ǫβi ǫδI i bi δIi(δij + ǫ(∂ihj + ∂jhi)) \uf8f9 \uf8fb .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (56) This result is a case of only vector modes in this portion of decomposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Extending the action to second order vector perturbations,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' we obtain S(2) V = � dt d3k (2π)3 � 4k4Ahihi + E ˙βi ˙βi + k2(4B ˙hi( ˙hi − bi) + Cbibi + Dβiβi + 4Fhiβi + 4Ghi ˙βi − 2Hβibi) � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (57) where A = GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='Tvec + 1 9X � −GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='J8 + XGTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='J6 − 5 2GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='J5 − 3GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='J3 � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' B = G4 − 2XG4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='X + XG5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='φ − GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='T + X � 2GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='J8 + 1 2GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='J5 � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' C = B + 1 2XGTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='J5 + 2 3XGTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='J10 + 2 9GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='Tax ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' D = C + XGTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='J5 − 2XGTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='J8 − 2XGTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='J10 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' E = 4A − 3GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='Tvec + 2XGTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='J3 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' F = 1 2 ˙φGTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='I2 − d dt (G4 − 2XG4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='X + XG5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='φ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' G = 2A − B − 3GTele,Tvec + 1 3XGTele,J3 − 2XGTele,J8 + 5 2XGTele,J5 , H = C − 2XGTele,J8 − 4 9GTele,Tax , (58) While the decomposition along unitary gauge ensures that there are no higher order time derivatives, one can see that the action contains higher order spatial derivatives [110].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Here, we will set the coefficients of these derivatives to vanish, but it should be noted that a general analysis for each constraint should be carried out before solving the next one and leading to a very complicate solution for the action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' By imposing the conditions A = 0 and B = 0, the latter condition accounting for the higher order mix of temporal and spatial derivatives [111], the action reduces to S(2) V = � dt d3k (2π)3 � E ˙βi ˙βi + k2(Cbibi + Dβiβi + 4Fhiβi + 4Ghi ˙βi − 2Hβibi) � , (59) where bi and hi are auxiliary vector modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' By varying with respect to each of these non-dynamical modes, the respective field equations are given by 2k2(Cbi − Hβi) = 0 , and 4k2Fβi = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (60) By solving for each auxiliary field and plugging it back in into Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (59), we get S(2) V = � dt d3k (2π)3 � E ˙βi ˙βi − k2 � H2 C − D � βiβi � , (61) wherein the action is expressed in terms of the dynamical non-gauge invariant mode βi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Thus the ghost and Laplacian conditions are given respectively by MV = E > 0 , and NV = H2 C − D > 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (62) suggesting that there is a propagating vector mode with speed cV = H2 − CD CE .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (63) This propagating mode generally steps from the introduction of the Ji terms in the BDLS action (27) representing the quadratic contractions of the scalar and torsion fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 11 a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Vanishing Ji terms: When considering the case were J1 = J3 = J5 = J6 = J10 = 0, the action (61) reduces to Svanishing J terms V = � dt d3k (2π)3 k2 � C − H2 C � βiβi , (64) exhibiting no dynamical modes i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' no propagating vector mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' In the case of only teleparallel function, the same conditions apply with vanishing Horndeski terms in each constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The subcases of standard Horndeski [31, 104], f( R) [99, 112], Generalized Brans-Dicke[108] and f(T ) [98] fall under this category of non-viable propagating vector mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' C = 0 : The Laplacian constraint, given in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (62), is undefined for C = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' By considering this particular case, the action results in SC=0 V = � dt d3k (2π)3 E ˙βi ˙βi , (65) to which the Laplacian condition is violated since it is null.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' On the other hand, imposing only E = 0, the ghost instability is generated since this value should be a positive definite value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Ji terms only: On the other hand, when considering only the contribution of the quadratic contrac- tions, the only surviving term is that with coefficient E leading to a ghost stability condition but leading to Laplacian instability, similar to the C = 0 case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' This implies the importance of having a combination of the Ji terms along with the rest of the teleparallel scalar invariants to maintain stability conditions and a possible propagating vector mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Constant Background Scalar Field: With regards to the scalar field, the unitary gauge is applied to the perturbative part of the scalar, while, at background level, it is a function of time only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Alternatively, if one considers a constant scalar field φ = c, then the entire action is vanishing such that no vector modes propagate, thus it corresponds to the results in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [67] for the DoF and polarisation modes in the vector portion of the decomposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Scalar Perturbations Let us now consider the scalar modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Since there is no mixing between the scalar and pseudoscalar modes, we will treat them separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The tetrad perturbation using scalar modes is given by eA µ → \uf8ee \uf8f01 + ϕ 0 δI i ∂ib (1 − ψδIiδij .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' \uf8f9 \uf8fb (66) As already stated, for the gauge invariant quantities, given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (47), the gauge choice is β = h = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The pseudoscalar will be analyzed separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' It should be noted that this situation is identical to the Arnowitt- Deser-Misner (ADM) decomposition used in torsion-based theories [100].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' It leads to the same metric as that applied to curvature-based theories [101].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' On the other hand, the choice β = b = 0 results in the Newtonian (longitudinal) gauge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Substituting the tetrad perturbation to the action,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' followed by integration by parts and application of the background equations (35-37),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' the second order perturbation of the action is given by S(2) S = � dt d3k (2π)3 � ¯ Aϕ2 + 6 ¯Dψ2 − 6 ¯F ˙ψ2 − 6 ¯Gϕ ˙ψ − k2(− ¯Bϕ2 − 2 ¯Eψ2 + 4 ¯Hϕψ − 2 ¯Gϕb − 4 ¯F ˙ψb) + k4 ¯Cb2� (67) 12 where ¯ A = XG2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='X + 2X2G2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='XX − 2XG3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='φ − 2X2G3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='φX + XGTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='X + 2X2GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='XX ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' ¯B = GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='Tvec + 2 9X (2GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='J8 + 2XGTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='J6 − 5GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='J5 + 3GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='J3) ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' ¯C = −GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='Tvec + XGTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='I2I2 + 1 3X(4GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='J8 + GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='J5) ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' ¯D = d dt( ˙φGTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='I2) ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' ¯E = G4 − X(G5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='φ − ¨φG5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='X) − GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='T + 2GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='Tvec + 1 9X (−2GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='J8 + 2XGTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='J6 − 5GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='J5 − 6GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='J3) ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' ¯F = G4 − 2XG4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='X + XG5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='φ − GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='T + 3 2(GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='Tvec − XGTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='I2I2) ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' ¯G = − ˙φXG3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='X + ˙φG4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='φ + 2 ˙φXG4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='φX + 1 2 ˙φGTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='I2 + ˙φXGTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='XI2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' ¯H = G4 − 2XG4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='X + XG5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='φ − GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='T + GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='Tvec + 1 9X(2GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='J8 − 2XGTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='J6 + 5GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='J5 + 3 2GTele,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='J3) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (68) Here k is the co-vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' As shown in coefficient of ¯C in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (67), there is a higher derivative contribution, hence it is set to vanish [110].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' It is clear that variables ϕ and b are non-dynamical with respect to the time component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' By varying with respect to each of these auxiliary fields, one obtains a set of equations 0 = ( ¯ A + k2 ¯B)ϕ − 3 ¯G ˙ψ + k2(2 ¯Hψ − ¯Gb) , (69) 0 = ¯Gϕ + 2 ¯F ˙ψ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (70) By solving these equations of motion for the modes ϕ and b, it leads to an action expressed in terms of the dynamical mode only, that is S(2) S = � dt d3k (2π)3 � 4k2 ¯B ¯F 2 ¯G 2 ˙ψ2 + � 4 ¯ A ¯F 2 ¯G 2 + 6 ¯F � ˙ψ2 − k2 � −2 ¯E + 4 d dt � ¯F ¯H ¯G �� ψ2 + 6 ¯Dψ2 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (71) Taking into account the mix of spatial and temporal higher-order derivatives, the first term of the action vanishes [111].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' This implies that either ¯F = 0 (which renders the whole action without a dynamical mode), or ¯B = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' By applying the latter condition, the action can be expressed in terms of a gauge invariant quantity within a Minkowski background and no higher-order terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' It is S(2) S = � dt d3k (2π)3 �� 4 ¯ A ¯F 2 ¯G 2 + 6 ¯F � ˙ψ2 − k2 � −2 ¯E + 4 d dt � ¯F ¯H ¯G �� ψ2 + 6 ¯Dψ2 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (72) In the case of teleparallel analogue of Horndeski theory, ghost stability and gradient stability are obtained, respectively, when MS = 4 ¯ A ¯F 2 ¯G 2 + 6 ¯F > 0 , (73) ¯ N S = −2 ¯F + 4 d dt � ¯F ¯H ¯G � > 0 , (74) and the propagating speed is cS = NS MS .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (75) Different subcases are reported in Table II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Through the substitution of Eqs (73) and (74), conditions to avoid ghost and Laplacian instabilities are realised.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Horndeski: The standard Horndeski case has identical expressions for ghost and gradient stability conditions as those for teleparallel Horndeski (73-74) with the difference that each constant does not have teleparallel contributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 13 b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Generalized Brans-Dicke: Considering Generalised Brans-Dicke (GBD) theory means that G2 = B(φ)X, G3 = 2Xξ(φ), G4 = 1 2F(φ) and all other terms are set to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' When we take the background equations B − 4Xξ′ = 0 , and ˙φ2F ′′ + ¨φ(F ′ − 2 ˙φ2ξ) = 0 , (76) for ghost stability, we have MGBD S = F[3F ′2 − 4 ˙φ2(Fξ′ + 3ξF ′) + 12 ˙φ4ξ2] [F ′ − 2 ˙φ2ξ]2 > 0 , (77) where ′ denotes a derivative with respect to the respective variable of the function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' In this case, it is φ, while the gradient condition is N GBD S = F[3F ′3 − 2 ˙φ2(5F ′2ξ − 4ξFF ′′ − 2Fξ′F ′) + 4 ˙φ4(F ′ξ2 − 2Fξ′ξ) + 8 ˙φ6ξ3] [F ′ − 2 ˙φ2ξ]3 > 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (78) With these conditions, the speed of propagation is positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' It is (cGBD S )2 = 3F ′3 − 2 ˙φ2(5F ′2ξ − 4ξFF ′′ − 2Fξ′F ′) + 4 ˙φ4(F ′ξ2 − 2Fξ′ξ) + 8 ˙φ6ξ3 [3F ′2 − 4 ˙φ2(Fξ′ + 3ξF ′) + 12 ˙φ4ξ2][F ′ − 2 ˙φ2ξ] , (79) which correlates with results obtained in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [108] for a Minkowski background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Brans-Dicke: As for the Brans-Dicke theory in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [107] with G2 = 2wBDX φ and G4 = φ, ghosts instabilities are avoided if 2φ(3 + 2wBD) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Provided that φ > 0, this implies that the Brans-Dicke constant is wBD > − 3 2 [99].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The gradient stability condition is given by 2φ(3 − 2φ¨φ/ ˙φ2) > 0 to ensure a positive propagating speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Moreover, when applying the second Friedman Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (36), gradient condition reduces to 2φ(3 + wBD) such that wBD > −3 and a unitary propagating speed [113], analogous to ξ = 0, reported in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [108], is obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The first Friedman Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (35) shows that the only non-trivial solution is that for wBD = 0, which results in identical ghost and gradient expressions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' f(˚ R): The scalar-tensor theory equivalent to f(R) [114] is given by setting G2 = f(φ) − φf ′(φ) and G4 = f ′(φ) while the rest of the functions are set to vanish.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' See also Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [73].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' In order to have ghost stability, it has to be 6f ′(φ) > 0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' f ′(φ) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Once again, upon applying the background Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (35-36), the gradient condition reduces to f ′(φ) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' In fact, as a subcase of GBD theory, the case ξ = 0 always results in a unitary speed propagating mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' GR, f(T ), f(φ, T ): When considering the cases of GR, f(T ) and f(φ, T ), the substitution in Eqs˜(73- 74) results in an undefined expression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' In these cases, although taking the appropriate limits of each coeffi- cient does lead to a positive ghost condition value, the propagating speed is negative, thus scalar modes are not viable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' This is expected in GR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Additionally, Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [98] shows that the only propagating scalar field is that dependent on the perturbation of scalar field φ, while, in this paper, we are applying the unitary gauge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' As in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [100], f(φ, T ) theory gives rise to a propagating mode when considering cosmological perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The same applies for GR with an additional canonical scalar field such that G2 = X − V (φ), G4 = M 2 Pl/2, G3 = G5 = GTele = 0 [101].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Teleparallel: If one considers only the teleparallel portions of the action, all terms from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (71) are retained, with all standard Horndeski contributions set to vanish.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' This implies that the ghost and Laplacian instabilities coincide with the form of Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (73) and (51), respectively, provided that the background equations are satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Pseudoscalar Perturbations The gauge invariant pseudoscalar σ can be treated separately as eA µ → \uf8ee \uf8f01 0 0 δIi(δij + ǫ εijk∂kσ) \uf8f9 \uf8fb ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (80) 14 Theory Case MS NS Horndeski GTele = 0 6 ¯ F + 4 ¯ A ¯ F2 ¯ G2 −2 ¯ E + 4 d dt ( ¯ F2 ¯ G ) Generalized Brans-Dicke GTele = G5 = 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' G2 = B(φ)X,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' G3 = 2ξ(φ)X,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' G4 = 1 2 F (φ) F [3F ′2−4 ˙φ2(F ξ′+3ξF′)+12 ˙φ4ξ2] [F ′−2 ˙φ2ξ]2 F [3F ′3−2 ˙φ2(5F ′2ξ−4ξFF ′′−2F ξ′F ′)+4 ˙φ4(F ′ξ2−2F ξ′ξ)+8 ˙φ6ξ3] [F ′−2 ˙φ2ξ]3 Brans-Dicke GTele = G3 = G5 = 0 G2 = 2wBDX φ ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' G4 = φ 2φ(3 + 2wBD) 2(3φ − ¨ φ X ) → 2φ(3 + 2wBD) f( ◦ R) GTele = G3 = G5 = 0 G2 = f(φ) − φf′(φ),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' G4 = f′(φ) 6f′(φ) −2f′(φ) + 4 d dt ( f′(φ)2 ˙φf′′(φ) ) → 6f′(φ) GR GTele = G2 = G3 = G5 = 0 G4 = 1 no propagating mode f(T ) G2 = G3 = G4 = G5 = 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' GTele = f(T ) no propagating mode f(φ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' T ) + XP (φ) G3 = G4 = G5 = 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' G2 = XP (φ),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' GTele = f(φ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' T ) no propagating mode Teleparallel G2 = G3 = G4 = G5 = 0 4 ¯ A ¯ F2 ¯ G2 + 6 ¯ F −2 ¯ F + 4 d dt � ¯ F ¯ H ¯ G � TABLE II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' List of literature models with the respective ghost MS and gradient stability NS conditions are positive definite, and propagation speed cS = NS/MS for scalar modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The models include Horndeski theory [20, 101, 104, 105], Generalized Brans-Dicke [108] and Brans-Dicke [107], f(˚ R) theory , General Relativity, f(T ) theory [98], f(φ, T ) theory [100].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' and an action with only teleparallel terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The action in Fourier space is expanded up to second order S(2) PS = − � dt d3k (2π)3 �� k2 d dt( ˙φGTele,I2) + 4 9k4 (GTele,Tax − 2XGTele,J1) � σ2 +k2 �4 9GTele,Tax + X � GTele,J5 + 4 3GTele,J10 �� ˙σ2 � , (81) where the first term exhibits higher-order spatial derivatives and the second term exhibits higher order mixed derivatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' By imposing that GTele,Tax = 2XGTele,J1 = −X � 9 4GTele,J5 + 3GTele,J10 � , the action reduces to S(2) PS = � dt d3k (2π)3 � − k2 d dt( ˙φGTele,I2)σ2� , (82) where σ is a non-dynamical mode and thus it is a non-propagating mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' This shows that in Minkowski background, the additional scalar invariants, provided by teleparallel analogue of Horndeski theory, do not contribute to any additional propagating DoF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' See also Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [98].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' DISCUSSION AND CONCLUSIONS We have investigated constraints emerging by considering the stability of perturbations about a Minkowski background in teleparallel analogue of Horndeski gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The approach is performed by exploring the ghost instabilities through looking at potentially negative expressions of kinetic term associated with propagating DoFs, as well as Laplacian instabilities emerging when propagation speeds of perturbations are not positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' This leads to possible exponential growth rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' These considerations are fundamental for the construction of robust and self-consistent cosmological models related to the scalar-tensor gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Specifically, we have discussed teleparallel analogue of Horndeski gravity where the most general scalar- tensor action is considered, provided that the Lagrangian terms are not parity violating and that scalars are produced by no more than quadratic contractions of torsion scalar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The naturally lower order nature of teleparallel gravity induces a much richer landscape of functional models when compared with standard metric Horndeski gravity, based on Levi-Civita connection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' In other words, the replacement of torsion with curvature to lead dynamics turns out to manifest as a generalization of the standard Horndeski theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Im- portantly, this produces a generalization of tensor mode propagation speed which means that the restrictions appearing in standard Horndeski gravity, due to the constraints on the gravitational waves speed, do not have the same effect here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 15 Our calculations have proceeded by first deriving the background equations of motion (35–37) which are obtained by considering a flat FLRW background in which we take the Minkowski limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' We find this to be a convenient approach to determine the system of equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' These are useful equations for reducing the expressions of perturbations that ensue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The procedure is described in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' We then proceeded to directly determine constraints to prevent ghost or Laplacian instabilities starting with tensor modes which results in the action in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (53) and tensor propagation speed in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (54).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' We collected the constraints for popular subclasses of BDLS theory in Table I where the known results are obtained for standard Horndeski gravity as well as f( R) and Brans-Dicke gravity, but new conditions are found in other cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' As for the vector perturbations, Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' V B shows that vector modes are indeed propagating for some cases of GTele contribution, namely when Ji scalars appear in this function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' However, these contributions may be small and within observational constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' The scalar perturbations contain the most diverse range of DoFs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' This rich structure produces the intricate action in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (72), together with the propagation speed in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' (75).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' As in the case of tensor modes, constraints for each subclass of popular models is reported in Table II where results for the Minkowski perturbations are recovered for standard metric Horndeski gravity together with f( R) and Brans-Dicke gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Interestingly, either no constraints are set on some of the purely teleparallel models or only lightly limited cases are set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Importantly, these constraints are consistent with the tensor mode constraints on the functional models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' These results are promising in terms of the viability of BDLS theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' As future work, it is intriguing to explore constraints from tachyonic instabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' These constraints have been connected to Jeans instability where exponential growth of perturbations is slowed by the expansion of the Universe and where the matter dispersion relation has a negative mass term that renders it to vanish.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' This could lead to a more general consideration of perturbations about a flat FLRW background spacetime which would then be directly linked to observations such as those related to the growth of large scale structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' In forthcoming studies, possible observational constraints will be scrutinized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' ACKNOWLEDGMENTS This paper is based upon work from COST Action CA21136 Addressing observational tensions in cosmology with systematics and fundamental physics (CosmoVerse) supported by COST (European Cooperation in Science and Technology).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' SC acknowledges the Istituto Nazionale di Fisica Nucleare (iniziative specifiche QGSKY and MOONLIGHT2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' MC acknowledges funding by the Tertiary Education Scholarship Scheme (TESS, Malta).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [1] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Misner, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Thorne, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Thorne, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Wheeler, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Freeman, and Company, Gravitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' pt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 3 in Gravitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Freeman, 1973.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' https://books.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='google.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='com.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='mt/books?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='id=w4Gigq3tY1kC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [2] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Clifton, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Ferreira, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Padilla, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Skordis, “Modified Gravity and Cosmology,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 513 (2012) 1–189, arXiv:1106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='2476 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [3] Supernova Search Team Collaboration, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Riess et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=', “Observational evidence from supernovae for an accelerating universe and a cosmological constant,” Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 116 (1998) 1009–1038, arXiv:astro-ph/9805201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [4] Supernova Cosmology Project Collaboration, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Perlmutter et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=', “Measurements of Ω and Λ from 42 high redshift supernovae,” Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 517 (1999) 565–586, arXiv:astro-ph/9812133.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [5] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Weinberg, “The Cosmological Constant Problem,” Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 61 (1989) 1–23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [6] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Appleby and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Linder, “The Well-Tempered Cosmological Constant,” JCAP 07 (2018) 034, arXiv:1805.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='00470 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [7] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Ishak, “Testing General Relativity in Cosmology,” Living Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 22 (2019) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 1, 1, arXiv:1806.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='10122 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [8] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Bernal, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Verde, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Riess, “The trouble with H0,” JCAP 10 (2016) 019, arXiv:1607.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='05617 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [9] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Di Valentino et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=', “Snowmass2021 - Letter of interest cosmology intertwined II: The hubble constant tension,” Astropart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 131 (2021) 102605, arXiv:2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='11284 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [10] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Di Valentino, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Mena, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Pan, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Visinelli, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Yang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Melchiorri, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Mota, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Riess, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Silk, “In the realm of the Hubble tension—a review of solutions,” Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 38 (2021) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 15, 153001, arXiv:2103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='01183 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 16 [11] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Riess, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Casertano, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Yuan, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Macri, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Scolnic, “Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛCDM,” Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 876 (2019) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 1, 85, arXiv:1903.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='07603 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [12] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Wong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=', “H0LiCOW – XIII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' A 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='4 per cent measurement of H0 from lensed quasars: 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='3σ tension between early- and late-Universe probes,” Mon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Roy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 498 (2020) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 1, 1420–1439, arXiv:1907.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='04869 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [13] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Riess et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=', “A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−1 Mpc−1 Uncertainty from the Hubble Space Telescope and the SH0ES Team,” Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 934 (2022) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 1, L7, arXiv:2112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='04510 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [14] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Brout et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=', “The Pantheon+ Analysis: SuperCal-fragilistic Cross Calibration, Retrained SALT2 Light-curve Model, and Calibration Systematic Uncertainty,” Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 938 (2022) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 2, 111, arXiv:2112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='03864 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [15] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Scolnic et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=', “The Pantheon+ Analysis: The Full Data Set and Light-curve Release,” Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 938 (2022) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 2, 113, arXiv:2112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='03863 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [16] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Abdalla et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=', “Cosmology intertwined: A review of the particle physics, astrophysics, and cosmology associated with the cosmological tensions and anomalies,” JHEAp 34 (2022) 49–211, arXiv:2203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='06142 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [17] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Di Valentino et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=', “Cosmology Intertwined III: fσ8 and S8,” Astropart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 131 (2021) 102604, arXiv:2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='11285 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [18] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Capozziello, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Benetti, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Spallicci, “Addressing the cosmological H0 tension by the Heisenberg uncertainty,” Found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 50 (2020) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 9, 893–899, arXiv:2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='00462 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [19] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Capozziello and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Faraoni, Beyond Einstein Gravity: A Survey of Gravitational Theories for Cosmology and Astrophysics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Springer, Dordrecht, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [20] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Horndeski, “Second-order scalar-tensor field equations in a four-dimensional space,” Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 10 (1974) 363–384.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [21] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Woodard, “Avoiding dark energy with 1/r modifications of gravity,” Lect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Notes Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 720 (2007) 403–433, arXiv:astro-ph/0601672.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [22] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Motohashi and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Suyama, “Third order equations of motion and the Ostrogradsky instability,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' D 91 (2015) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 8, 085009, arXiv:1411.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='3721 [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='class-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [23] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Pagani, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Tecchiolli, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Zerbini, “On the Problem of Stability for Higher Order Derivatives: Lagrangian Systems,” Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 14 (1987) 311.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [24] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Miranda, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Vernieri, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Capozziello, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Faraoni, “Generalized McVittie geometry in Horndeski gravity with matter,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' D 105 (2022) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 12, 124024, arXiv:2204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='09693 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [25] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Miranda, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Vernieri, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Capozziello, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Faraoni, “Fluid nature constrains Horndeski gravity,” arXiv:2209.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='02727 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [26] LIGO Scientific, Virgo Collaboration, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Abbott et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=', “GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 119 (2017) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 16, 161101, arXiv:1710.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='05832 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [27] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Goldstein et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=', “An Ordinary Short Gamma-Ray Burst with Extraordinary Implications: Fermi-GBM Detection of GRB 170817A,” Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 848 (2017) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 2, L14, arXiv:1710.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='05446 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='HE].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [28] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Kobayashi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Yamaguchi, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Yokoyama, “Generalized G-inflation: Inflation with the most general second-order field equations,” Prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 126 (2011) 511–529, arXiv:1105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='5723 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [29] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Gleyzes, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Langlois, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Piazza, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Vernizzi, “Essential Building Blocks of Dark Energy,” JCAP 08 (2013) 025, arXiv:1304.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='4840 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [30] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Koyama, “Cosmological Tests of Modified Gravity,” Rept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 79 (2016) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 4, 046902, arXiv:1504.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='04623 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [31] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Kobayashi, “Horndeski theory and beyond: a review,” Rept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 82 (2019) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 8, 086901, arXiv:1901.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='07183 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [32] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Bahamonde, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Dialektopoulos, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Escamilla-Rivera, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Farrugia, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Gakis, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Hendry, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Hohmann, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Said, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Mifsud, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Di Valentino, “Teleparallel Gravity: From Theory to Cosmology,” arXiv:2106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='13793 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [33] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Aldrovandi and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Pereira, Teleparallel Gravity: An Introduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Springer, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [34] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Cai, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Capozziello, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' De Laurentis, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Saridakis, “f(T) teleparallel gravity and cosmology,” Rept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 79 (2016) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 10, 106901, arXiv:1511.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='07586 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [35] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Krssak, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' van den Hoogen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Pereira, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' B¨ohmer, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Coley, “Teleparallel theories of gravity: illuminating a fully invariant approach,” Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 36 (2019) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 18, 183001, arXiv:1810.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='12932 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [36] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Lovelock, “The Einstein tensor and its generalizations,” J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 12 (1971) 498–501.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [37] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Gonzalez and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Vasquez, “Teleparallel Equivalent of Lovelock Gravity,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' D 92 (2015) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 12, 124023, arXiv:1508.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='01174 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 17 [38] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Bahamonde, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Dialektopoulos, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Levi Said, “Can Horndeski Theory be recast using Teleparallel Gravity?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=',” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' D 100 (2019) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 6, 064018, arXiv:1904.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='10791 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [39] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Capozziello, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' De Falco, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Ferrara, “Comparing equivalent gravities: common features and differences,” Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' C 82 (2022) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 10, 865, arXiv:2208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='03011 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [40] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Ferraro and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Fiorini, “Modified teleparallel gravity: Inflation without inflaton,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' D 75 (2007) 084031, arXiv:gr-qc/0610067.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [41] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Ferraro and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Fiorini, “On Born-Infeld Gravity in Weitzenbock spacetime,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' D 78 (2008) 124019, arXiv:0812.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='1981 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [42] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Bengochea and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Ferraro, “Dark torsion as the cosmic speed-up,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' D 79 (2009) 124019, arXiv:0812.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='1205 [astro-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [43] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Linder, “Einstein’s Other Gravity and the Acceleration of the Universe,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' D 81 (2010) 127301, arXiv:1005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='3039 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [Erratum: Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='D 82, 109902 (2010)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [44] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Dent, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Dutta, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Saridakis, “Cosmological perturbations in f(T) gravity,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' D 83 (2011) 023508, arXiv:1008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='1250 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [45] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Bahamonde, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Flathmann, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Pfeifer, “Photon sphere and perihelion shift in weak f(T ) gravity,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' D 100 (2019) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 8, 084064, arXiv:1907.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='10858 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [46] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rezaei Akbarieh and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Izadi, “Tachyon Inflation in Teleparallel Gravity,” Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' C 79 (2019) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 4, 366, arXiv:1812.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='06649 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [47] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Bahamonde, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' B¨ohmer, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Wright, “Modified teleparallel theories of gravity,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' D 92 (2015) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 10, 104042, arXiv:1508.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='05120 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [48] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Bahamonde and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Capozziello, “Noether Symmetry Approach in f(T, B) teleparallel cosmology,” Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' C 77 (2017) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 2, 107, arXiv:1612.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='01299 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [49] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Paliathanasis, “de Sitter and Scaling solutions in a higher-order modified teleparallel theory,” JCAP 08 (2017) 027, arXiv:1706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='02662 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [50] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Farrugia, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Levi Said, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Gakis, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Saridakis, “Gravitational Waves in Modified Teleparallel Theories,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' D 97 (2018) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 12, 124064, arXiv:1804.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='07365 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [51] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Bahamonde, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Zubair, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Abbas, “Thermodynamics and cosmological reconstruction in f(T, B) gravity,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Dark Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 19 (2018) 78–90, arXiv:1609.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='08373 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [52] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Wright, “Conformal transformations in modified teleparallel theories of gravity revisited,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' D 93 (2016) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 10, 103002, arXiv:1602.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='05764 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [53] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Farrugia, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Levi Said, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Finch, “Gravitoelectromagnetism, Solar System Tests, and Weak-Field Solutions in f(T, B) Gravity with Observational Constraints,” Universe 6 (2020) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 2, 34, arXiv:2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='08183 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [54] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Capozziello, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Capriolo, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Caso, “Weak field limit and gravitational waves in f(T, B) teleparallel gravity,” Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' C 80 (2020) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 2, 156, arXiv:1912.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='12469 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [55] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Escamilla-Rivera and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Levi Said, “Cosmological viable models in f(T, B) theory as solutions to the H0 tension,” Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 37 (2020) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 16, 165002, arXiv:1909.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='10328 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [56] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Capozziello, “Curvature quintessence,” Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' D 11 (2002) 483–492, arXiv:gr-qc/0201033.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [57] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Sotiriou and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Faraoni, “f(R) Theories Of Gravity,” Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 82 (2010) 451–497, arXiv:0805.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='1726 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [58] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Faraoni, “f(R) gravity: Successes and challenges,” in 18th SIGRAV Conference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 10, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' arXiv:0810.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='2602 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [59] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Capozziello and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' De Laurentis, “Extended Theories of Gravity,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 509 (2011) 167–321, arXiv:1108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='6266 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [60] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Nojiri and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Odintsov, “Introduction to modified gravity and gravitational alternative for dark energy,” eConf C0602061 (2006) 06, arXiv:hep-th/0601213.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [61] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Nojiri and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Odintsov, “Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 505 (2011) 59–144, arXiv:1011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='0544 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [62] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Nojiri, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Odintsov, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Oikonomou, “Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 692 (2017) 1–104, arXiv:1705.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='11098 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [63] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Hohmann, “Scalar-torsion theories of gravity I: general formalism and conformal transformations,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' D 98 (2018) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 6, 064002, arXiv:1801.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='06528 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [64] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Hohmann and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Pfeifer, “Scalar-torsion theories of gravity II: L(T, X, Y, φ) theory,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' D 98 (2018) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 6, 064003, arXiv:1801.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='06536 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [65] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Hohmann, “Scalar-torsion theories of gravity III: analogue of scalar-tensor gravity and conformal invariants,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' D 98 (2018) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 6, 064004, arXiv:1801.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='06531 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [66] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Bahamonde, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Dialektopoulos, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Gakis, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Levi Said, “Reviving Horndeski theory using teleparallel gravity after GW170817,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' D 101 (2020) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 8, 084060, arXiv:1907.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='10057 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [67] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Bahamonde, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Caruana, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Dialektopoulos, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Gakis, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Hohmann, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Levi Said, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Saridakis, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Sultana, “Gravitational-wave propagation and polarizations in the teleparallel analog of Horndeski gravity,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' D 104 (2021) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 8, 084082, arXiv:2105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='13243 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 18 [68] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Ezquiaga and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Zumalac´arregui, “Dark Energy After GW170817: Dead Ends and the Road Ahead,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 119 (2017) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 25, 251304, arXiv:1710.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='05901 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [69] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Bahamonde, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Dialektopoulos, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Hohmann, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Levi Said, “Post-Newtonian limit of Teleparallel Horndeski gravity,” Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 38 (2020) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 2, 025006, arXiv:2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='11554 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [70] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Bernardo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Said, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Caruana, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Appleby, “Well-tempered teleparallel Horndeski cosmology: a teleparallel variation to the cosmological constant problem,” JCAP 10 (2021) 078, arXiv:2107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='08762 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [71] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Bernardo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Said, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Caruana, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Appleby, “Well-tempered Minkowski solutions in teleparallel Horndeski theory,” Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 39 (2022) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 1, 015013, arXiv:2108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='02500 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [72] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Capozziello, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' De Laurentis, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Dialektopoulos, “Noether symmetries in Gauss–Bonnet-teleparallel cosmology,” Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' C 76 (2016) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 11, 629, arXiv:1609.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='09289 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [73] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Capozziello, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Dialektopoulos, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Sushkov, “Classification of the Horndeski cosmologies via Noether Symmetries,” Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' C 78 (2018) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 6, 447, arXiv:1803.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='01429 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [74] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Dialektopoulos and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Capozziello, “Noether Symmetries as a geometric criterion to select theories of gravity,” Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Geom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Meth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 15 (2018) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' supp01, 1840007, arXiv:1808.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='03484 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [75] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Dialektopoulos, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Said, and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Oikonomopoulou, “Classification of teleparallel Horndeski cosmology via Noether symmetries,” Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' C 82 (2022) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 3, 259, arXiv:2112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='15045 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [76] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Bajardi and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Capozziello, Noether Symmetries in Theories of Gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Cambridge Monographs on Mathematical Physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Cambridge University Press, 11, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [77] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Hehl, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Von Der Heyde, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Kerlick, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Nester, “General Relativity with Spin and Torsion: Foundations and Prospects,” Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 48 (1976) 393–416.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [78] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Krˇsˇs´ak and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Saridakis, “The covariant formulation of f(T) gravity,” Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 33 (2016) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 11, 115009, arXiv:1510.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='08432 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [79] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Weitzenb¨ock, Invariantentheorie.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Noordhoff, Groningen, 1923.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [80] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Aldrovandi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Barros, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Pereira, “Spin and anholonomy in general relativity,” arXiv:gr-qc/0402022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [81] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Hayashi and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Shirafuji, “New General Relativity,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' D 19 (1979) 3524–3553.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [Addendum: Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='D 24, 3312–3314 (1982)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [82] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Capozziello, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Lambiase, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Stornaiolo, “Geometric classification of the torsion tensor in space-time,” Annalen Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 10 (2001) 713–727, arXiv:gr-qc/0101038.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [83] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Bahamonde, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' B¨ohmer, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Krˇsˇs´ak, “New classes of modified teleparallel gravity models,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' B 775 (2017) 37–43, arXiv:1706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='04920 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [84] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Nesseris, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Basilakos, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Saridakis, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Perivolaropoulos, “Viable f(T ) models are practically indistinguishable from ΛCDM,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' D 88 (2013) 103010, arXiv:1308.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='6142 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [85] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Koivisto, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Hohmann, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Marzola, “Axiomatic derivation of coincident general relativity and its premetric extension,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' D 103 (2021) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 6, 064041, arXiv:1909.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='10415 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [86] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Hehl, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' McCrea, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Mielke, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Ne’eman, “Metric affine gauge theory of gravity: Field equations, Noether identities, world spinors, and breaking of dilation invariance,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 258 (1995) 1–171, arXiv:gr-qc/9402012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [87] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Beltr´an Jim´enez, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Heisenberg, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Koivisto, “The Geometrical Trinity of Gravity,” Universe 5 (2019) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 7, 173, arXiv:1903.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='06830 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [88] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Beltr´an Jim´enez, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Heisenberg, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Koivisto, “The coupling of matter and spacetime geometry,” Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 37 (2020) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 19, 195013, arXiv:2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='04606 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [89] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Bahamonde, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Gakis, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Kiorpelidi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Koivisto, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Levi Said, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Saridakis, “Cosmological perturbations in modified teleparallel gravity models: Boundary term extension,” Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' C 81 (2021) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 1, 53, arXiv:2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='02168 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [90] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Abedi and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Capozziello, “Gravitational waves in modified teleparallel theories of gravity,” Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' C 78 (2018) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 6, 474, arXiv:1712.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='05933 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [91] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Abedi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Capozziello, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' D’Agostino, and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Luongo, “Effective gravitational coupling in modified teleparallel theories,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' D 97 (2018) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 8, 084008, arXiv:1803.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='07171 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [92] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Wu and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='-Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Geng, “Matter Density Perturbations in Modified Teleparallel Theories,” JHEP 11 (2012) 142, arXiv:1211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='1778 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [93] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Dent, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Dutta, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Saridakis, “Cosmological perturbations in f(T) gravity,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' D 83 (2011) 023508, arXiv:1008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='1250 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [94] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Bruni, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Matarrese, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Mollerach, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Sonego, “Perturbations of space-time: Gauge transformations and gauge invariance at second order and beyond,” Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 14 (1997) 2585–2606, arXiv:gr-qc/9609040.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [95] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Malik and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Wands, “Cosmological perturbations,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 475 (2009) 1–51, arXiv:0809.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='4944 [astro-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [96] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Nakamura, “Gauge-invariant formulation of the second-order cosmological perturbations,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' D 74 (2006) 101301, arXiv:gr-qc/0605107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 19 [97] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Hohmann, “General cosmological perturbations in teleparallel gravity,” Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Plus 136 (2021) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 1, 65, arXiv:2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='02491 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [98] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Izumi and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Ong, “Cosmological Perturbation in f(T) Gravity Revisited,” JCAP 06 (2013) 029, arXiv:1212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='5774 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [99] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' De Felice and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Tsujikawa, “f(R) theories,” Living Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 13 (2010) 3, arXiv:1002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='4928 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [100] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Gonzalez-Espinoza, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Otalora, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Saavedra, “Stability of scalar perturbations in scalar-torsion f(T,φ) gravity theories in the presence of a matter fluid,” JCAP 10 (2021) 007, arXiv:2101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='09123 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [101] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Kobayashi, “Horndeski theory and beyond: a review,” Rept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 82 (2019) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 8, 086901, arXiv:1901.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='07183 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [102] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Bahamonde, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Caruana, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Dialektopoulos, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Gakis, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Hohmann, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Levi Said, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Saridakis, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Sultana, “Gravitational-wave propagation and polarizations in the teleparallel analog of Horndeski gravity,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' D 104 (2021) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 8, 084082, arXiv:2105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='13243 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [103] LIGO Scientific, Virgo Collaboration, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Abbott et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=', “GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 119 (2017) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 16, 161101, arXiv:1710.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='05832 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [104] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' De Felice and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Tsujikawa, “Conditions for the cosmological viability of the most general scalar-tensor theories and their applications to extended Galileon dark energy models,” JCAP 02 (2012) 007, arXiv:1110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='3878 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [105] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Kobayashi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Yamaguchi, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Yokoyama, “Generalized G-inflation: Inflation with the most general second-order field equations,” Prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 126 (2011) 511–529, arXiv:1105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='5723 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [106] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Gao and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Steer, “Inflation and primordial non-Gaussianities of ’generalized Galileons’,” JCAP 12 (2011) 019, arXiv:1107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='2642 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [107] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Brans and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Dicke, “Mach’s principle and a relativistic theory of gravitation,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 124 (1961) 925–935.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [108] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' De Felice and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Tsujikawa, “Generalized Brans-Dicke theories,” JCAP 07 (2010) 024, arXiv:1005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='0868 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [109] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Hohmann, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' J¨arv, and U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Ualikhanova, “Covariant formulation of scalar-torsion gravity,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' D 97 (2018) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 10, 104011, arXiv:1801.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='05786 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [110] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Gleyzes, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Langlois, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Piazza, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Vernizzi, “Essential Building Blocks of Dark Energy,” JCAP 08 (2013) 025, arXiv:1304.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='4840 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [111] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Gergely and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Tsujikawa, “Effective field theory of modified gravity with two scalar fields: dark energy and dark matter,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' D 89 (2014) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 6, 064059, arXiv:1402.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='0553 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [112] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Capozziello and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' De Felice, “f(R) cosmology by Noether’s symmetry,” JCAP 08 (2008) 016, arXiv:0804.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='2163 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [113] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' ¨Ozer and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Delice, “Gravitational waves in Brans–Dicke theory with a cosmological constant,” Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' C 81 (2021) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 4, 326, arXiv:2101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content='03594 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' [114] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Teyssandier and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Tourrenc, “The Cauchy problem for the R+R**2 theories of gravity without torsion,” J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'} +page_content=' 24 (1983) 2793.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENE3T4oBgHgl3EQfVQoB/content/2301.04457v1.pdf'}