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

Extending the current standard analysis of the galaxy power spectrum to include the bispectrum represents a significant step towards extracting the full cosmological information from galaxy redshift surveys. 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 a simple perturbation theory. In particular, we compute the 5- and 6-point spectra to predict the cross-covariance between the power and bispectra, and the auto-covariance of the bispectrum. To quantify the redshift-space distortion effect, we focus especially on the monopole and quadrupole components of both the power and bispectra. 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 find that the leading-order perturbation theory only with the linear bias are in remarkable agreement with the measurements from the mock catalogues up to $k\sim0.2\hk$, and can reproduce the cumulative signal-to-noise ratios of the power spectrum and the bispectrum jointly measured from the mock catalogues. Our analytic model also provides a theoretical insight to the shot noise effect in the power spectrum and bispectrum covariances and cross-covariance.