# Perturbation theory approach to predict the covariance matrices of the galaxy power spectrum and bispectrum in redshift space

## TL;DR

This paper develops a perturbation theory-based method to accurately predict the covariance matrices of galaxy power spectrum and bispectrum in redshift space, including non-Gaussian effects, and validates it against mock catalogues.

## Contribution

First to compute 5- and 6-point spectra for cross- and auto-covariances in redshift space using perturbation theory, improving covariance predictions for galaxy clustering analysis.

## Key findings

- PT model reproduces the signal-to-noise ratio well up to certain scales.
- Simple leading-order PT suffices due to dominant shot-noise effects.
- Discrepancies in cross-covariance suggest areas for further refinement.

## Abstract

In this paper, we predict the covariance matrices of both the power spectrum and the bispectrum, including full non-Gaussian contributions, redshift space distortions, linear bias effects and shot-noise corrections, using perturbation theory (PT). To quantify the redshift-space distortion effect, we focus mainly on the monopole and quadrupole components of both the power and bispectra. We, for the first time, compute the 5- and 6-point spectra to predict the cross-covariance between the power and bispectra, and the auto-covariance of the bispectrum in redshift space. We test the validity of our calculations by comparing them with the covariance matrices measured from the MultiDark-Patchy mock catalogues that are designed to reproduce the galaxy clustering measured from the Baryon Oscillation Spectroscopic Survey Data Release 12. We argue that the simple, leading-order perturbation theory works because the shot-noise corrections for the Patchy mocks are more dominant than other higher-order terms we ignore. In the meantime, we confirm some discrepancies in the comparison, especially of the cross-covariance. We discuss potential sources of such discrepancies. We also show that our PT model reproduces well the cumulative signal-to-noise of the power spectrum and the bispectrum as a function of maximum wavenumber, implying that our PT model captures successfully essential contributions to the covariance matrices.