Robustness of the covariance matrix for galaxy clustering measurements

TL;DR

This study assesses how the covariance matrix for galaxy clustering measurements depends on cosmological parameters and galaxy bias, finding it reliable at large scales but biased at small scales when 3-point statistics are mismatched.

Contribution

It demonstrates that the covariance matrix is insensitive to the input power spectrum but biased at small scales if 3-point statistics are inconsistent, emphasizing the importance of accurate 3-point modeling.

Findings

Covariance matrix is insensitive to the input power spectrum.

Bias appears at small scales when 3-point statistics are incompatible.

At large scales, the covariance matrix remains reliable for data analysis.

Abstract

We present a study on the robustness of the covariance matrix estimation for galaxy clustering measurements depending on the cosmological parameters and galaxy bias. To this end, we have produced 9000 galaxy mock catalogues relying on the effective Zel'dovich approximation implemented in the EZmocks computer code, using different input cosmological models and bias parameters. The reference catalogue has also been produced with this code making our study insensitive to the approximation at least on a relative-qualitative level. Our findings indicate that the covariance matrix is insensitive to the input power spectrum (including $\sigma_8$), as long as the 2- and 3-point galaxy clustering measurements agree with the given data. In fact, the covariance matrix shows a bias at small scales ($r\lesssim40 h^{-1}$Mpc) when the chosen galaxy bias parameters yield a 3-point statistics, which is not compatible with the reference one within the error bars, even though the 2-point statistics agree within 1%. Nevertheless, the error becomes negligible at large scales making the covariance matrix still reliable for data analysis using only measurements in that regime (e.g., measuring baryon acoustic oscillations). High precision in cosmological parameter estimation is expected for covariance matrices extracted from mock galaxy catalogues which take accurately into account both the 2- and the 3- point statistics. This is independent of whether this is achieved by using the right cosmology and galaxy bias (which are not a priori known) or just any combination of both fitting the net observed galaxy clustering.