Gaussian covariance matrices for anisotropic galaxy clustering measurements

TL;DR

This paper introduces a simple theoretical Gaussian model for the covariance of anisotropic galaxy clustering measurements, validated against synthetic catalogues, to improve covariance estimation with limited simulations.

Contribution

It provides explicit formulas for covariance matrices in Fourier and configuration space, enabling accurate, fast covariance estimates for galaxy clustering analyses.

Findings

Model predictions agree well with synthetic data in the quasi-linear regime.

The approach reduces reliance on extensive N-body simulations for covariance estimation.

Validates the Gaussian approximation for anisotropic clustering covariance in certain regimes.

Abstract

Measurements of the redshift-space galaxy clustering have been a prolific source of cosmological information in recent years. Accurate covariance estimates are an essential step for the validation of galaxy clustering models of the redshift-space two-point statistics. Usually, only a limited set of accurate N-body simulations is available. Thus, assessing the data covariance is not possible or only leads to a noisy estimate. Further, relying on simulated realisations of the survey data means that tests of the cosmology dependence of the covariance are expensive. With these points in mind, this work presents a simple theoretical model for the linear covariance of anisotropic galaxy clustering observations with synthetic catalogues. Considering the Legendre moments (`multipoles') of the two-point statistics and projections into wide bins of the line-of-sight parameter (`clustering wedges'), we describe the modelling of the covariance for these anisotropic clustering measurements for galaxy samples with a trivial geometry in the case of a Gaussian approximation of the clustering likelihood. As main result of this paper, we give the explicit formulae for Fourier and configuration space covariance matrices. To validate our model, we create synthetic HOD galaxy catalogues by populating the haloes of an ensemble of large-volume N-body simulations. Using linear and non-linear input power spectra, we find very good agreement between the model predictions and the measurements on the synthetic catalogues in the quasi-linear regime.