An efficient model of cosmology dependence in the covariance matrix of the matter power spectrum

TL;DR

This paper introduces a fast, Taylor expansion-based model to estimate how the covariance matrix of the matter power spectrum varies with cosmological parameters, significantly reducing computational costs.

Contribution

The authors develop a novel interpolation method for the covariance matrix dependence on cosmology, requiring only a few input cosmologies and avoiding extensive calculations for each new parameter set.

Findings

The model accurately reproduces covariance matrices across different cosmologies.

Interpolation speeds up calculations by orders of magnitude.

The method remains robust with various approximations and corrections.

Abstract

Covariance matrices are essential cosmological probes of fundamental physics, providing information on numerous fundamental physical parameters and varying with any change in the underlying cosmology. However, this cosmology dependence, while providing excellent information, also makes them computationally intensive to compute, as a new covariance matrix must explicitly be calculated for every variation in cosmology before comparisons to observational data can be made. In this paper, we develop an efficient model for estimating the parameter dependence of the covariance matrix of the matter power spectrum by Taylor expanding around a known value of the parameter space. This method allows us to use a relatively small number of input cosmologies, specifically one fiducial cosmology and two further cosmologies for each parameter. We explicitly calculate the covariance matrices for these cosmologies and then develop a new model that allows us to interpolate from these the form of the covariance matrix with a cosmology that is located elsewhere in that given parameter space without explicit perturbation theory calculations. This method speeds up covariance matrix calculations in new cosmologies by orders of magnitude compared to explicit perturbation theory calculations at each point in a given parameter space. Using different approximations, we develop three versions of our interpolated covariance matrix and validate the model by recreating all of our input cosmologies using all three forms, both with and without super-sample covariance corrections in each case, and show that the models provide robust recreations of the original results, with the different approximations being valid in certain regimes.