Modelling galaxy clustering on small scales to tighten constraints on dark energy and modified gravity

We present a new approach to measuring cosmic expansion history and growth rate of large-scale structure using the anisotropic two-dimensional galaxy correlation function (2DCF) measured from data; it makes use of the empirical modelling of small-scale galaxy clustering derived from numerical simulations by Zheng et al. We validate this method using mock catalogues, before applying it to the analysis of the CMASS sample from the Sloan Digital Sky Survey Data Release 10 of the Baryon Oscillation Spectroscopic Survey. We find that this method enables accurate and precise measurements of cosmic expansion history and growth rate of large-scale structure. Modelling the 2DCF fully including non-linear effects and redshift space distortions in the scale range of 16–144 h^(−1) Mpc, we find H(0.57)rs(zd)/c = 0.0459 ± 0.0006, DA(0.57)/rs(zd) = 9.011 ± 0.073, and fg(0.57)σ8(0.57) = 0.476 ± 0.050, which correspond to precisions of 1.3 per cent, 0.8 per cent, and 10.5 per cent, respectively. We have defined rs(zd) to be the sound horizon at the drag epoch computed using a simple integral, fg(z) as the growth rate at redshift z, and σ8(z) as the matter power spectrum normalization on 8 h^(−1) Mpc scale at z. We find that neglecting the small-scale information significantly weakens the constraints on H(z) and DA(z), and leads to a biased estimate of fg(z). Our results indicate that we can significantly tighten constraints on dark energy and modified gravity by reliably modelling small-scale galaxy clustering