Modelling the covariance matrix for the power spectra before and after the BAO reconstruction

TL;DR

This paper models the covariance matrix of power spectra before and after BAO reconstruction using perturbation theory, validating the model against simulations and highlighting non-Gaussian effects.

Contribution

It introduces an analytical covariance model for pre- and post-BAO reconstructed power spectra, incorporating non-Gaussian effects and validated with simulations.

Findings

Gaussian prediction works well for diagonal auto covariance

Cross covariance deviates from Gaussian at high k values

Non-Gaussian contributions improve covariance estimation

Abstract

The baryon acoustic oscillation (BAO) reconstruction plays a crucial role in cosmological analysis for spectroscopic galaxy surveys because it can make the density field effectively more linear and more Gaussian. The combination of the power spectra before and after the BAO reconstruction helps break degeneracies among parameters, then improve the constraints on cosmological parameters. It is therefore important to estimate the covariance matrix between pre- and post-reconstructed power spectra. In this work, we use perturbation theory to estimate the covariance matrix of the related power spectra multipoles, and check the accuracy of the derived covariance model using a large suite of dark matter halo catalogs at $z=0.5$. We find that the diagonal part of the auto covariance is well described by the Gaussian prediction, while the cross covariance deviates from the Gaussian prediction quickly when $k > 0.1\,h\,\mathrm{Mpc}^{-1}$. Additionally, we find the non-Gaussian effect in the non-diagonal part of the cross covariance is comparable to, or even stronger than the pre-reconstruction covariance. By adding the non-Gaussian contribution, we obtain good agreement between analytical and numerical covariance matrices in the non-diagonal part up to $k \simeq 0.15\,h\,\mathrm{Mpc}^{-1}$. The agreement in the diagonal part is also improved, but still under-predicts the correlation in the cross covariance block.