A model of the anisotropic correlation function xi(rp, pi) in redshift space including redshift errors

TL;DR

This paper introduces a new model for the anisotropic galaxy correlation function in redshift space that accounts for nonlinear effects and redshift errors, validated against simulations, to improve dark energy constraints.

Contribution

The authors develop and validate a comprehensive model of xi(rp, pi) that incorporates nonlinear growth, velocities, and redshift errors, enabling unbiased dark energy parameter estimation.

Findings

Model accurately reproduces correlation function shape in simulations.

Unbiased constraints on dark energy w_DE achievable with redshift errors up to 0.06.

Model performance confirmed for large survey volumes and typical galaxy densities.

Abstract

With the advent of very large volume, wide-angle photometric redshift surveys like e.g. Pan-STARRS, DES, or PAU, which aim at using the spatial distribution of galaxies as a means to constrain the equation of state parameter of dark energy, w_DE, it has become extremely important to understand the influence of redshift inaccuracies on the measurement. We have developed a new model for the anisotropic two point large-scale (r > 64 h^-1 Mpc) correlation function xi(rp,pi), in which nonlinear structure growth and nonlinear coherent infall velocities are taken into account, and photometric redshift errors can easily be incorporated. In order to test its validity and investigate the effects of photometric redshifts, we compare our model with the correlation function computed from a suite of 50 large-volume, moderate-resolution numerical N-body simulation boxes, where we can perform the analysis not only in real- and redshift space, but also simulate the influence of a gaussian redshift error distribution with an absolute rms of sigma_z= 0.015, 0.03, 0.06, and 0.12, respectively. We conclude that for the given volume (V_box =2.4 h^-3 Gpc^3) and number density (n ~ 1.25 10^-4) of objects the full shape of xi(rp,pi) is modeled accurately enough to use it to derive unbiased constraints on the equation of state parameter of dark energy w_DE and the linear bias b, even in the presence of redshift errors of the order of sigma_z = 0.06.