On the Systematic Errors of Cosmological-Scale Gravity Tests using Redshift Space Distortion: Non-linear Effects and the Halo Bias

TL;DR

This study evaluates the systematic errors in measuring the growth rate of cosmic structures using redshift space distortion, emphasizing the importance of non-linear effects and halo bias, and proposes methods to reduce these errors for future surveys.

Contribution

It introduces an analytical RSD model that accounts for higher-order effects and a scale-dependent bias, significantly reducing systematic errors in cosmological measurements.

Findings

Systematic error in $f\sigma_8$ reduced to ~5% with advanced RSD modeling.

The scale-dependent bias model improves accuracy across different halo masses and redshifts.

Wilson-Hilferty transformation enhances likelihood analysis with limited data modes.

Abstract

Redshift space distortion (RSD) observed in galaxy redshift surveys is a powerful tool to test gravity theories on cosmological scales, but the systematic uncertainties must carefully be examined for future surveys with large statistics. Here we employ various analytic models of RSD and estimate the systematic errors on measurements of the structure growth-rate parameter, $f\sigma_8$, induced by non-linear effects and the halo bias with respect to the dark matter distribution, by using halo catalogues from 40 realisations of $3.4 \times 10^8$ comoving $h^{-3}$Mpc$^3$ cosmological N-body simulations. We consider hypothetical redshift surveys at redshifts z=0.5, 1.35 and 2, and different minimum halo mass thresholds in the range of $5.0 \times 10^{11}$ -- $2.0 \times 10^{13} h^{-1} M_\odot$. We find that the systematic error of $f\sigma_8$ is greatly reduced to ~5 per cent level, when a recently proposed analytical formula of RSD that takes into account the higher-order coupling between the density and velocity fields is adopted, with a scale-dependent parametric bias model. Dependence of the systematic error on the halo mass, the redshift, and the maximum wavenumber used in the analysis is discussed. We also find that the Wilson-Hilferty transformation is useful to improve the accuracy of likelihood analysis when only a small number of modes are available in power spectrum measurements.