Dependence of cosmic shear covariances on cosmology - Impact on parameter estimation

TL;DR

This paper investigates how cosmic shear covariance matrices vary with cosmological parameters and demonstrates that assuming a constant covariance can bias likelihood analyses, proposing adaptive and iterative methods to improve accuracy.

Contribution

It quantifies the dependence of cosmic shear covariances on cosmology and introduces two methods to incorporate this dependence into parameter estimation.

Findings

Covariances vary significantly within the parameter range.

Assuming constant covariance affects likelihood contours.

Adaptive covariance improves accuracy but is computationally intensive.

Abstract

In cosmic shear likelihood analyses the covariance is most commonly assumed to be constant in parameter space. Therefore, when calculating the covariance matrix (analytically or from simulations), its underlying cosmology should not influence the likelihood contours. We examine whether the aforementioned assumption holds and quantify how strong cosmic shear covariances vary within a reasonable parameter range. Furthermore, we examine the impact on likelihood contours when assuming different cosmologies in the covariance. We find that covariances vary significantly within the considered parameter range (Omega_m=[0.2;0.4], sigma_8=[0.6;1.0]) and that this has a non-negligible impact on the size of likelihood contours. This impact increases with increasing survey size, increasing number density of source galaxies, decreasing ellipticity noise, and when using non-Gaussian covariances. To improve on the assumption of a constant covariance we present two methods. The adaptive covariance is the most accurate method, but it is computationally expensive. To reduce the computational costs we give a scaling relation for covariances. As a second method we outline the concept of an iterative likelihood analysis. Here, we additionally account for non-Gaussianity using a ray-tracing covariance derived from the Millennium simulation.