Covariance of the redshift-space matter power spectrum after reconstruction

TL;DR

This paper investigates how density-field reconstruction reduces covariance in redshift-space matter power spectra, leading to improved signal-to-noise ratio and more accurate growth rate measurements, supported by perturbative theory and N-body simulations.

Contribution

It derives a perturbative formula for the covariance after reconstruction and demonstrates the reduction of off-diagonal covariance components through simulations, showing enhanced information recovery.

Findings

Reconstruction decreases off-diagonal covariance components.

Post-reconstruction spectra have higher S/N than linear Gaussian spectra.

Reconstruction improves growth rate estimation accuracy.

Abstract

We explore the covariance of redshift-space matter power spectra after a standard density-field reconstruction. We derive perturbative formula of the covariance at the tree-level order and find that the amplitude of the off-diagonal components from the trispectrum decreases by reconstruction. Using a large set of N-body simulations, we also find the similar reduction of the off-diagonal components of the covariance and thereby the signal-to-noise ratio (S/N) of the post-reconstructed (post-rec) power spectra significantly increases compared to the pre-reconstructed spectra. This indicates that the information leaking to higher-order statistics come back to the two-point statistics by reconstruction. Interestingly, the post-rec spectra have higher S/N than the linear spectrum with Gaussian covariance when the scale of reconstruction characterized with the smoothing scale of the shift field is below ~10Mpc/h where the trispectrum becomes negative. We demonstrate that the error of the growth rate estimated from the monopole and quadrupole components of the redshift-space matter power spectra significantly improves by reconstruction. We also find a similar improvement of the growth rate even when taking into account the super-sample covariance, while the reconstruction cannot correct for the field variation of the super-sample modes.