Constraining scale dependent growth with redshift surveys

Abstract

Ongoing and future redshift surveys have the capability tomeasure the growth rate of large scale structure at thepercent level over a broad range of redshifts, tightlyconstraining cosmological parameters. Beyond generalrelativity, however, the growth rate in the linear densityperturbation regime can be not only redshift dependent butscale dependent, revealing important clues to modified gravity.We demonstrate that a fully model independent approach of binningthe gravitational strength G eff (k,z) matchesscalar-tensor results for the growth rate fσ 8(k,z) to0.02%–0.27% rms accuracy. For data of the quality ofthe Dark Energy Spectroscopic Instrument (DESI) we find thebin values can be constrained to 1.4%–28%. We alsoexplore thegeneral scalar-tensor form, constraining the amplitude andpast and future scalaron mass/shape parameters.Perhaps most interesting is the strong complementarityof low redshift peculiar velocity data with DESI-likeredshift space distortion measurements, enablingimprovements up to a factor 6–7 on 2D joint confidencecontour areas.Finally, we quantify some issues with gravityparametrizations that do not include all the key physics.