Euclid preparation. XXVII. Covariance model validation for the 2-point correlation function of galaxy clusters

TL;DR

This paper validates a semi-analytical covariance model for the 2-point correlation function of galaxy clusters, demonstrating its accuracy and the importance of cosmology-dependent covariance for Euclid survey constraints.

Contribution

It introduces a simple, calibrated covariance model that accurately predicts clustering covariance and highlights the benefits of including cosmology dependence and mass binning.

Findings

The Gaussian Poissonian model underestimates covariance.

The calibrated model achieves 10% accuracy in covariance prediction.

Cosmology-dependent covariance improves parameter constraints.

Abstract

Aims. We validate a semi-analytical model for the covariance of real-space 2-point correlation function of galaxy clusters. Methods. Using 1000 PINOCCHIO light cones mimicking the expected Euclid sample of galaxy clusters, we calibrate a simple model to accurately describe the clustering covariance. Then, we use such a model to quantify the likelihood analysis response to variations of the covariance, and investigate the impact of a cosmology-dependent matrix at the level of statistics expected for the Euclid survey of galaxy clusters. Results. We find that a Gaussian model with Poissonian shot-noise does not correctly predict the covariance of the 2-point correlation function of galaxy clusters. By introducing few additional parameters fitted from simulations, the proposed model reproduces the numerical covariance with 10 per cent accuracy, with differences of about 5 per cent on the figure of merit of the cosmological parameters $\Omega_{\rm m}$ and $\sigma_8$. Also, we find that the cosmology-dependence of the covariance adds valuable information that is not contained in the mean value, significantly improving the constraining power of cluster clustering. Finally, we find that the cosmological figure of merit can be further improved by taking mass binning into account. Our results have significant implications for the derivation of cosmological constraints from the 2-point clustering statistics of the Euclid survey of galaxy clusters.