Improving the precision matrix for precision cosmology

TL;DR

This paper evaluates a covariance tapering technique to improve the estimation of the precision matrix in cosmology, reducing the number of mock catalogues needed for accurate parameter constraints.

Contribution

It introduces and tests a novel covariance tapering method that reduces noise in the precision matrix estimation without biasing results, aiding future large-scale surveys.

Findings

Covariance tapering reduces the impact of noise in the precision matrix.

The method allows for accurate cosmological constraints with fewer mock catalogues.

No biases are introduced in the parameter estimation.

Abstract

The estimation of cosmological constraints from observations of the large scale structure of the Universe, such as the power spectrum or the correlation function, requires the knowledge of the inverse of the associated covariance matrix, namely the precision matrix, $\mathbf{\Psi}$. In most analyses, $\mathbf{\Psi}$ is estimated from a limited set of mock catalogues. Depending on how many mocks are used, this estimation has an associated error which must be propagated into the final cosmological constraints. For future surveys such as Euclid and DESI, the control of this additional uncertainty requires a prohibitively large number of mock catalogues. In this work we test a novel technique for the estimation of the precision matrix, the covariance tapering method, in the context of baryon acoustic oscillation measurements. Even though this technique was originally devised as a way to speed up maximum likelihood estimations, our results show that it also reduces the impact of noisy precision matrix estimates on the derived confidence intervals, without introducing biases on the target parameters. The application of this technique can help future surveys to reach their true constraining power using a significantly smaller number of mock catalogues.