Euclid: The linear-construction covariance and cosmology

TL;DR

This paper evaluates the linear-construction method for estimating galaxy cluster covariance matrices, demonstrating it provides comparable cosmological parameter constraints to traditional methods with significantly reduced computational cost.

Contribution

The study introduces and validates the linear-construction covariance estimation method for cosmology, showing it matches the accuracy of standard sample covariance in parameter inference.

Findings

LC method is up to 20 times faster than sample covariance.

Parameter estimates from LC and sample covariance agree within uncertainties.

LC method accurately reproduces cosmological constraints from mock data.

Abstract

We study the properties of galaxy cluster 2-point correlation function covariance matrices estimated using the linear-construction (LC) method, which is computationally up to 20 times faster than the standard sample-covariance method. Our goal is to assess how well the LC method performs in cosmological parameter estimation compared to the sample covariance. We use a set of 1000 mock dark matter halo catalogues to compute both the LC-covariance and the sample-covariance estimates in four redshift shells. These numerical matrices are used to fit a theoretical four-parameter model for the covariance. We then use the two fitted covariance models in a likelihood function to estimate two cosmological parameters - the matter density parameter $\Omega_{\rm m}$ and the amplitude of the matter density fluctuations $\sigma_8$ - from the simulated mock catalogues. The purpose of this is to validate the LC-covariance-based model against the sample-covariance model. The catalogues were simulated assuming the spatially flat $\Lambda$CDM cosmology, with $\Omega_{\rm m} = 0.30711$ and $\sigma_8=0.8288$. We find that the parameter posteriors obtained using the sample- and LC-covariance models agree well with each other and with the simulation cosmology. The two pairs of marginalized constraints are $\Omega_{\rm m} = 0.307 \pm 0.003$ and $\sigma_8 = 0.826\pm 0.009$ (sample covariance), and $\Omega_{\rm m} = 0.308 \pm 0.003$ and $\sigma_8 = 0.825 \pm 0.009$ (LC covariance). The posterior widths are the same, and the difference in the median values is less than $0.16\,\sigma$ for both parameters.