Antide Sitter vacuum which correspond to a negative cosmological constant CC is theoretically important and wellmotivated. However whether it exists in reality or not has always been a controversial issue. In this paper we perform the search for the negative CC using recent Dark Energy Spectroscopic Instrument DESI baryon acoustic oscillation measurements combined with Planck cosmic microwave background and Pantheon Plus supernova data. Though we did not find the evidence for negative CC we observed the indication for it the negative CC is preferred at gt68 significance level while such a negative CC can make the state equation of evolving dark energy component coexisting with negative CC wgeqslant 1. Our work highlights the potential of upcoming cosmological surveys to search for the negative CC.
['Astrophysics - Cosmology and Nongalactic Astrophysics', 'General Relativity and Quantum Cosmology', 'High Energy Physics - Theory']
Can recent DESI BAO measurements accommodate a negative cosmological constant
{'Can recent DESI BAO measurements accommodate a negative cosmological constant?': 'Hao Wang 1 , 2 ∗ , Ze-Yu Peng 3 † , and Yun-Song Piao 1 , 2 , 3 , 4 ‡  \n1  \nSchool of Fundamental Physics and Mathematical Sciences,  \nHangzhou Institute for Advanced Study, UCAS, Hangzhou 310024, China  \n- 2 School of Physics Sciences, University of Chinese Academy of Sciences, Beijing 100049, China  \n3  \nInternational Center for Theoretical Physics Asia-Pacific, Beijing/Hangzhou, China and  \n4 Institute of Theoretical Physics, Chinese Academy of Sciences, P.O. Box 2735, Beijing 100190, China  \nAnti-de Sitter vacuum, which correspond to a negative cosmological constant (CC), is theoretically important and well-motivated. However, whether it exists in reality or not has always been a controversial issue. In this paper, we perform the search for the negative CC using recent Dark Energy Spectroscopic Instrument (DESI) baryon acoustic oscillation measurements combined with Planck cosmic microwave background and Pantheon Plus supernova data. Though we did not find the evidence for negative CC, we observed the indication for it, the negative CC is preferred at > 68% significance level, while such a negative CC can make the state equation of evolving dark energy component (coexisting with negative CC) w ⩾ -1. Our work highlights the potential of upcoming cosmological surveys to search for the negative CC.  \nPACS numbers:', 'I. INTRODUCTION': 'The concordance ΛCDM model is the simplest description of our universe, which can naturally explain most of cosmological and astrophysical observations. In corresponding model, Λ, also called the dark energy (DE), is responsible for the accelerated expansion of current universe. In the past decades, identifying the nature of DE has been still an important challenge, see e.g.[1-4] for reviews. It is usually thought that DE is a positive cosmological constant (CC), e.g.[5, 6]. However, recently DESI collaboration [7-9] using their first year baryon acoustic oscillation (BAO) data, combined with Planck cosmic microwave background (CMB) data, has found w 0 = -0 . 45 ± 0 . 27 and w a = -1 . 79 ± 0 . 79 for the parameterised equation of state of DE [10, 11]  \nw ( z ) = w 0 + w a z 1 + z , (1)  \nwhile when Pantheon data is considered, the constraints on w 0 and w a becomes tighter, w 0 = 0 . 827 ± 0 . 063 and w a = -0 . 75 ± 0 . 27, the CC ( w 0 = -1 and w a = 0) has been not preferred at > 2 σ C.L. see also [12, 13]. The relevant issues have been also intensively investigated recently, e.g.[14-31], see also [32].  \nIt is well-known that anti-de Sitter (AdS) vacuum, which correspond to a negative CC, is theoretically important and well-motivated. Though it is possible that dS vacua exist [33, 34], the construction of such vacua in string landscape is not straightforward, notably e.g. recent swampland conjecture [35, 36], see [37, 38] for recent reviews and also [39]. However, AdS vacua exist naturally in string landscape.  \nRecently, the impacts of AdS vacua on our observable universe have been investigated, in particular the resolution of the Hubble tension might be related to the AdS vacuum around the recombination [40-44], or the switchsign CC [45-49], see also [50]. The inflation in AdS landscape and its implication for primordial perturbations have been explored in e.g.[51-55]. Though a negative CC is unable to drive the acceleration of our universe, it can coexist with one evolving positive DE component, and the corresponding effects have been surveyed in light of cosmic microwave background (CMB) and pre-DESI BAOdataset [56-62], as well as recent James Webb Space Telescope (JWST) observations [63, 64].  \nThough the existence of AdS vacua could profoundly affect our understanding about the nature of DE and quantum gravity, whether it exists in reality or not has always been a controversial issue. In this paper, we perform the first search for the negative CC using recent DESI BAO measurements combined with Planck CMB and Pantheon Plus supernova data. Though we did not find the evidence for negative CC, we observed the indication for it, the negative CC is preferred at > 68% significance level, see Fig.1.', 'II. DATA AND METHODOLOGY': "To perform the search for the negative CC using recent observations, we adopt the following observational datasets:  \n- · CMB Planck 2018 low-l and high-l TT, TE, EE spectra, and reconstructed CMB lensing spectrum [65-67].\n- · DESI BAO The measurements of DESI for the comoving distance D M /r d and D H /r d [7-9],  \nD M ( z ) ≡ ∫ z 0 cdz ' H ( z ' ) , D H ( z ) ≡ c H ( z ) , (2)  \nFIG. 1: The 1 σ and 2 σ contours of Ω L -Ω m with the Planck18+DESI+Pantheon Plus dataset, where Ω m is the current fraction of matter density and Ω L is that of the CC.  \n<!-- image -->  \nwhere r d = ∫ ∞ z d c s ( z ) H ( z ) is the sound horizon, z d ≃ 1060 is the redshift at the baryon drag epoch and c s is the speed of sound, as well as the angle-averaged quantity D V /r d where D V ( z ) ≡ ( zD M ( z ) 2 D H ( z ) ) 1 / 3 .  \nTABLE I: Statistics for the DESI samples of the DESI DR1 BAO measurements used in this paper [9].  \n- · Pantheon+ We use Pantheon+ consisting of 1701 light curves of 1550 spectroscopically confirmed type Ia SN coming from 18 different surveys [68].  \nHere, we assumed that one CC and one evolving positive DE component coexist, called the w 0 w a CDM+CC model for simplicity, where the state equation w x ( z ) of positive-energy component of DE follows (1). They are related by Ω m + Ω r + Ω x + Ω Λ = 1, where the current fraction of the matter density Ω m , the radiation Ω r , the evolving positive-energy component of DE Ω x and the CC Ω L .  \nThe parameter space of the w 0 w a CDM+CC model adapted is { 100 ω b , ω cdm , H 0 , n s , ln 10 10 A s , τ reio , w 0 , w a , Ω x } . There is only an additional parameter Ω x , compared with the w 0 w a CDM model, while that of the CC component is related to Ω x by Ω Λ = 1 -Ω m -Ω r -Ω x . We modified the MontePython-3.6 sampler [69, 70] and CLASS codes [71, 72] to perform our MCMC analysis. In Table.II we list the flat priors used. We adopt a Gelman-Rubin convergence criterion with a threshold R -1 < 0 . 01.  \nTABLE II: The priors of parameters we adapt in MCMC analysis. w 0 , eff and w a , eff are defined in (4) and (5).", 'III. RESULTS': 'In Table.III and IV, we present our MCMC results and the corresponding χ 2 . As in the w 0 w a CDM model, for the w 0 w a component of DE, w 0 = -1 and w a = 0 is still ruled out beyond ≳ 2 σ C.L.. However, a negative CC (the bestfit Ω Λ ∼ -0 . 3) is preferred at > 1 σ C.L. by data (the fit is improved with ∆ χ 2 ∼ -1 . 1).  \nTABLE III: Mean (bestfit) values and 1 σ regions of the parameters of w 0 w a CDM+CC model. The dataset used is the Planck18+DESI+Pantheon Plus dataset.  \nTABLE IV: χ 2 of w 0 w a CDM and w 0 w a CDM+CC model.  \nFIG. 2: 1 σ and 2 σ contours of w 0 -w a for the w 0 w a CDM and w 0 w a CDM+CC models, respectively, and scattered plot for the w 0 w a CDM+CC model with respect to Ω Λ .  \n<!-- image -->  \nIn Fig.2, we find that compare to the w 0 w a CDM model, the 2 σ contour of w 0 -w a in the w 0 w a CDM+CC models shifts up as a whole, so that w a = 0 can be 1 σ consistent with the observations, which is an unexpected result. This can be explained as follows. In our case, the low-redshift evolution of background is co-controlled by the evolving DE component Ω x with the state equation w x and CC Ω Λ , beside the matter, it is interesting to consider an effective state equation of w 0 w a +CC DE [63] 1  \nw eff ( z ) = Ω x (1 + z ) 2+3 w 0 +3 w a [ w 0 +( w 0 + w a ) z ] e -3 waz 1+ z -Ω x (1 + z ) 3(1+ w 0 + w a ) e -3 waz 1+ z +Ω Λ (3)  \ninstead of w x . Analogous to the parameterization (1), we have  \nw 0 , eff ≡ w eff ( z ) | z =0 = Ω x w 0 -Ω Λ Ω x +Ω Λ , (4)  \nand  \nw a , eff ≡ dw eff ( z ) dz | z =0 = Ω x [ w a Ω x +3( w 0 +1) 2 Ω Λ ] (Ω x +Ω Λ ) 2 . (5)  \nIt can be observed that for Ω Λ < 0, we will have w 0 , eff > w 0 and w a , eff < w a (noting Ω x +Ω Λ = 1 -Ω m -Ω r ∼ 0 . 7). Thus if w 0 , eff > -1 and w a , eff < 0 supported by observations, w 0 and w a must be closer to w 0 = -1 and w a = 0, which is just the result showed in Fig.2.  \nThe reason that an moderate negative CC with the bestfit Ω Λ ∼ -0 . 3 is preferred by Planck18+DESI+Pantheon Plus dataset is that it  \nΩ  \nsuggests w 0 , eff ∼ -0 . 8 and w a , eff ∼ -0 . 7 at low redshift, as reported by the DESI collaboration for the w 0 w a CDM model. However, the inclusion of a negative CC in a positive w 0 w a DE component can make w 0 > -1 and w a ∼ 0 (so we can always have w ⩾ -1) 1 σ consistent. The negative CC component with | Ω Λ | ∼ O (1) has been also considered in e.g. Refs.[56, 57, 60, 63].  \nIn Fig.3, we show the evolutions of D H ( z ) /r d , D M ( z ) /r d and D V ( z ) /r d for our bestfit values, in which Ω Λ = -0 . 316. It is found that a negative CC could slightly suppress D H ( z ) /r d , D M ( z ) /r d and D V ( z ) /r d at low redshift, and notably the negative CC can bring a slightly better fitting at the effective redshift z eff = 0 . 51 (see e.g.the comments in Refs.[16, 20, 22, 23] on DESI data at z eff = 0 . 51) and z eff = 0 . 71, which might be responsible to the improvement of ∆ χ 2 DESI ∼ -0 . 6, see Table.IV. This result can be explained as follows. According to the parameterization (1), for a negative Ω Λ , we have  \nH 2 ( z ) H 2 0 = Ω m (1 + z ) 3 -| Ω Λ | +(1 -Ω m + | Ω Λ | )(1 + z ) 3(1+ w 0 + w a ) e -3 waz 1+ z . (6)  \nThus ρ x ( z ) = ρ 0 (1 -Ω m + | Ω Λ | )(1 + z ) 3(1+ w 0 + w a ) e -3 waz 1+ z (so H ( z )) must be larger than that in the w 0 w a CDM model without negative CC, or else ρ x ( z ) + ρ Λ at low redshift will lower too fast to fit the observation. In certain sense the concavities of D H ( z ) /r d , D M ( z ) /r d and D V ( z ) /r d at low redshift might be an observable imprint  \nΛ  \n,  \nof negative CC (AdS vacuum), the upcoming more sur-  \nvey data would rule out it.', 'IV. DISCUSSION': 'In this paper, with recent DESI BAO data we found the indication for the negative CC, which is preferred at > 68% C.L.. The quintessence has been ruled out at ≳ 2 σ C.L. in recent DESI paper [9], however, an unexpected effect of our result is that the inclusion of a negative CC will make w 0 and w a for the evolving DE component (coexisting with negative CC) closer to w 0 = -1 and w a = 0, in particular, w 0 + w a ⩾ -1 (i.e. a quintessencelike component) can be 1 σ consistent.  \nIn our phenomenological study, we simply incorporate a negative CC into the parameterized w 0 w a CDM model, however, in realistic scalar field model it might be that the corresponding DE has an AdS vacuum, thus at low redshift it will roll towards the AdS vacuum, so that our universe will collapse at certain redshift z < 0. However, relevant scalar field phenomenology seems not so simple and might be richer than expected. The test for negative CC with the high-redshift JWST massive galaxies has been investigated in Refs.[63, 64]. How to combine the JWST and Planck+DESI+Pantheon+ data to search for the negative CC is also an interesting issue.  \nFIG. 3: Residuals of D H ( z ) /r d , D M ( z ) /r d and D V ( z ) /r d for the bestfit values (blue curves) of the w 0 w a CDM+CC model with respect to the w 0 w a CDM model. The blue shadows are the corresponding 1 σ regions.  \n<!-- image -->  \nIt should be mentioned that we also have considered our Planck18+DESI+Pantheon+ dataset combined with the SH0ES prior, which, however, only suggests H 0 ≃ 70 [74], thus it seems that such a low-redshift negative CC is not enough to solve the Hubble tension, and a prerecombination resolution might be still necessary, see also [75] for a recent model-independent test. Thus it is worth re-accessing the corresponding results in the Hubbletension-free cosmologies, as in recent Refs.[15, 30].', 'Acknowledgments': "This work is supported by NSFC, No.12075246, National Key Research and Development Program of China,  \n[1] J. 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