N-body simulations of gravitational redshifts and other relativistic distortions of galaxy clustering

TL;DR

This paper uses N-body simulations to predict and analyze relativistic effects, including gravitational redshift, on galaxy clustering patterns in large-scale structure surveys, emphasizing the importance of small-scale structures.

Contribution

It introduces a comprehensive simulation-based approach to quantify relativistic distortions in galaxy clustering, incorporating multiple effects at non-linear scales.

Findings

Relativistic effects cause measurable asymmetries in galaxy cross-correlation functions.

Gravitational redshift and luminosity distance perturbation dominate the observed asymmetries.

Small-scale galaxy structure significantly enhances the relativistic signal.

Abstract

Large redshift surveys of galaxies and clusters are providing the first opportunities to search for distortions in the observed pattern of large-scale structure due to such effects as gravitational redshift. We focus on non-linear scales and apply a quasi-Newtonian approach using N-body simulations to predict the small asymmetries in the cross-correlation function of two galaxy different populations. Following recent work by Bonvin et al., Zhao and Peacock and Kaiser on galaxy clusters, we include effects which enter at the same order as gravitational redshift: the transverse Doppler effect, light-cone effects, relativistic beaming, luminosity distance perturbation and wide-angle effects. We find that all these effects cause asymmetries in the cross-correlation functions. Quantifying these asymmetries, we find that the total effect is dominated by the gravitational redshift and luminosity distance perturbation at small and large scales, respectively. By adding additional subresolution modelling of galaxy structure to the large-scale structure information, we find that the signal is significantly increased, indicating that structure on the smallest scales is important and should be included. We report on comparison of our simulation results with measurements from the SDSS/BOSS galaxy redshift survey in a companion paper.