real and Fourier space 2-point statistics and the associated bias parameters for tracers of different masses for models beyond GR. The LPT predictions are compared to statistics derived from simulations in Section \[sec:Results:Compsims\]. Finally, we conclude, and discuss implications for future work, in Section \[sec:conclusions\]. More detail on the derivations in the paper are given in the Appendix.

Formalism {#sec:Formalism}
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Modified gravity models {#sec:Models}
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### The $f(R)$ model

Despite the latest surge in the field of MG, deformations to GR, together with associated experimental tests, have been around for almost as long as GR itself [@Will:2005va]. One of the oldest attempts consisted of adding a nonlinear function $f(R)$ of the Ricci scalar $R$ to the standard Einstein-Hilbert action, the so-called $f(R)$ theories [@DeFelice:2010aj], with a resulting action $S$ of the form: $$\label{actFr}
S=\int d^4x \sqrt{-g} \left[\frac{R+f(R)}{16 \pi G} + \mathcal{L}_m \right],$$ with $\mathcal{L}_m$ denoting the matter sector Lagrangian and G the gravitational constant. Since such an action frees up an additional degree of freedom, the latest interest in this class of theories comes from the idea that a modification of this type is responsible for cosmic acceleration, rather than dark energy [@Carroll:2003wy].

Such a model is the Hu-Sawicki 