Euclid: Effect of sample covariance on the number counts of galaxy clusters

TL;DR

This paper assesses how shot-noise and sample variance affect cosmological parameter constraints from galaxy cluster counts in the Euclid survey, validating an analytical covariance model and emphasizing the importance of cosmology-dependent likelihoods.

Contribution

It validates an analytical covariance model for cluster count uncertainties and demonstrates the necessity of using cosmology-dependent likelihoods for unbiased parameter inference.

Findings

Analytical covariance matches simulation variance within 10%.

Using cosmology-dependent covariance yields unbiased parameter estimates.

Gaussian likelihood with cosmology dependence is optimal for Euclid cluster analysis.

Abstract

Aims. We investigate the contribution of shot-noise and sample variance to the uncertainty of cosmological parameter constraints inferred from cluster number counts in the context of the Euclid survey. Methods. By analysing 1000 Euclid-like light-cones, produced with the PINOCCHIO approximate method, we validate the analytical model of Hu & Kravtsov 2003 for the covariance matrix, which takes into account both sources of statistical error. Then, we use such covariance to define the likelihood function that better extracts cosmological information from cluster number counts at the level of precision that will be reached by the future Euclid photometric catalogs of galaxy clusters. We also study the impact of the cosmology dependence of the covariance matrix on the parameter constraints. Results. The analytical covariance matrix reproduces the variance measured from simulations within the 10 per cent level; such difference has no sizeable effect on the error of cosmological parameter constraints at this level of statistics. Also, we find that the Gaussian likelihood with cosmology-dependent covariance is the only model that provides an unbiased inference of cosmological parameters without underestimating the errors.