Towards an accurate model of small-scale redshift-space distortions in modified gravity

Abstract: The coming generation of galaxy surveys will provide measurements of galaxy clustering with unprecedented accuracy and data size, which will allow us to test cosmological models at much higher precision than achievable previously. This means that we must have more accurate theoretical predictions to compare with future observational data. As a first step towards more accurate modelling of the redshift space distortions (RSD) of small-scale galaxy clustering in modified gravity (MG) cosmologies, we investigate the validity of the so-called Skew-T (ST) probability distribution function (PDF) of halo pairwise peculiar velocities in these models. We show that, combined with the streaming model of RSD, the ST PDF substantially improves the small-scale predictions by incorporating skewness and kurtosis, for both $\Lambda$CDM and two leading MG models: $f(R)$ gravity and the DGP braneworld model. The ST model reproduces the velocity PDF and redshift-space halo clustering measured from MG $N$-body simulations very well down to $\sim 5 \, h^{-1}\mathrm{Mpc}$. In particular, we investigate the enhancements of halo pairwise velocity moments with respect to $\Lambda$CDM for a larger range of MG variants than previous works, and present simple explanations to the behaviours observed. By performing a simple Fisher analysis, we find a significnat increase in constraining power to detect modifications of General Relativity by introducing small-scale information in the RSD analyses.