Direct Determination of Expansion History Using Redshift Distortions

We investigate direct determination of expansion history using redshift distortions without plugging into detailed cosmological parameters. The observed spectra in redshift space include a mixture of information: fluctuations of density-density and velocity-velocity spectra, and distance measures of perpendicular and parallel components to the line of sight. Unfortunately it is hard to measure all the components simultaneously without any specific prior assumption. Common prior assumptions include a linear/quasi-linear model of redshift distortions or a model for the shape of the power spectra, which eventually breaks down on small scales at later epochs where nonlinear structure formation disturbs coherent growth. The degeneracy breaking between the effect of cosmic distances and redshift distortions for example depends on the prior we assume. As an alternative approach is to utilize the cosmological principle inscribed in the heart of the Friedmann-Lemaître-Robertson-Walker (hereafter FLRW) universe, that is, the specific relation between the angular diameter distance and the Hubble parameter, in this degeneracy breaking. We show that utilizing this FLRW prior early in the step of distinguishing the distance effect from redshift distortions help us improve the detectability of power spectra and distance measures with no leaning on combination of other experiments.