Validation of semi-analytical, semi-empirical covariance matrices for two-point correlation function for Early DESI data

TL;DR

This paper validates semi-analytical and semi-empirical covariance matrices for the two-point correlation function using DESI LRG mock data, demonstrating their accuracy and potential to replace extensive mock catalog generation.

Contribution

It extends previous covariance formalism to include standard reconstruction algorithms and provides validation techniques for accurate covariance estimation without large mock samples.

Findings

Good agreement between predictions and sample covariance.

Covariance matrices can be generated from data measurements alone.

Validation techniques improve covariance accuracy for DESI-like datasets.

Abstract

We present an extended validation of semi-analytical, semi-empirical covariance matrices for the two-point correlation function (2PCF) on simulated catalogs representative of Luminous Red Galaxies (LRG) data collected during the initial two months of operations of the Stage-IV ground-based Dark Energy Spectroscopic Instrument (DESI). We run the pipeline on multiple effective Zel'dovich (EZ) mock galaxy catalogs with the corresponding cuts applied and compare the results with the mock sample covariance to assess the accuracy and its fluctuations. We propose an extension of the previously developed formalism for catalogs processed with standard reconstruction algorithms. We consider methods for comparing covariance matrices in detail, highlighting their interpretation and statistical properties caused by sample variance, in particular, nontrivial expectation values of certain metrics even when the external covariance estimate is perfect. With improved mocks and validation techniques, we confirm a good agreement between our predictions and sample covariance. This allows one to generate covariance matrices for comparable datasets without the need to create numerous mock galaxy catalogs with matching clustering, only requiring 2PCF measurements from the data itself. The code used in this paper is publicly available at https://github.com/oliverphilcox/RascalC.