Precision Redshift-Space Galaxy Power Spectra using Zel'dovich Control Variates

TL;DR

This paper extends Zel'dovich control variates to redshift-space galaxy power spectra, significantly reducing sample variance and improving the accuracy of clustering predictions in cosmological simulations.

Contribution

It introduces a novel application of Zel'dovich control variates to redshift-space 2-point statistics, enhancing simulation efficiency and accuracy.

Findings

Sample variance reduced to shot-noise limit up to k ~ 0.2 h/Mpc

Improved agreement between simulations and perturbative models

Enhanced predictions for galaxy and quasar clustering in surveys

Abstract

Numerical simulations in cosmology require trade-offs between volume, resolution and run-time that limit the volume of the Universe that can be simulated, leading to sample variance in predictions of ensemble-average quantities such as the power spectrum or correlation function(s). Sample variance is particularly acute at large scales, which is also where analytic techniques can be highly reliable. This provides an opportunity to combine analytic and numerical techniques in a principled way to improve the dynamic range and reliability of predictions for clustering statistics. In this paper we extend the technique of Zel'dovich control variates, previously demonstrated for 2-point functions in real space, to reduce the sample variance in measurements of 2-point statistics of biased tracers in redshift space. We demonstrate that with this technique, we can reduce the sample variance of these statistics down to their shot-noise limit out to $k \sim 0.2\, h\rm Mpc^{-1}$. This allows a better matching with perturbative models and improved predictions for the clustering of e.g.~quasars, galaxies and neutral Hydrogen measured in spectroscopic redshift surveys at very modest computational expense. We discuss the implementation of ZCV, give some examples and provide forecasts for the efficacy of the method under various conditions.