We compute the gravity model testing parameter $E_G$ (gravity estimator) on realistic simulated modified gravity galaxy mocks adopting the more accurate estimator described in [Z. Wang et al., J. Cosmol. Astropart. Phys. (2023) 038.]. The analysis is conducted using two twin simulations presented in [C. Arnold, M. Leo, and B. Li, Nat. Astron. 3, 917 (2019).]; one based on general relativity (GR) and the other on the $f(R)$ Hu and Sawicki model with $f={10}^{-5}$ (F5). This study aims to measure the $E_G$ estimator in GR and $f(R)$ models using high-fidelity simulated galaxy catalogs, with the goal of assessing how future galaxy surveys can detect deviations from standard gravity. Deriving this estimator requires precise, unbiased measurements of the growth rate of structure and the linear galaxy bias. We achieve this by implementing an end-to-end cosmological analysis pipeline in configuration space, using the multipoles of the two-point correlation function. In our analysis we estimate the scale-dependent growth rate predicted by nonstandard gravity models using COMET-VDG (cosmological observables modelled by emulated perturbation theory-velocity difference generator) fits. We split the estimation of the redshift space distortions (RSD) $\beta$ parameter over distinct scale ranges, separating large (quasilinear) and small (nonlinear) scales. We show that this estimator can be accurately measured using mock galaxies in low redshift bins ($z<1$), although its discriminating power between competing theories is limited. We find that, for an all-sky galaxy survey and neglecting observational systematics, accurate and largely unbiased estimations of $E_G$ can be obtained across all redshifts. However, the error bars are too large to clearly distinguish between the theories. When measuring the scale dependence of the $E_G$ estimator, we note that state-of-the-art theory modeling limitations and intrinsic “prior volume effects” prevent high-accuracy constraints. Alternatively, we propose a null test of gravity using RSD clustering, which, if small scales are modeled accurately in future surveys, could detect departures from GR.

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• Alternative gravity theories
• Cosmological parameters
• Dark energy
• General relativity
• Large scale structure of the Universe
• Galaxy clusters