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In this paper, we predict the covariance matrices of both the power spectrumand the bispectrum, including full non-Gaussian contributions, redshift spacedistortions, linear bias effects and shot-noise corrections, using perturbationtheory (PT). To quantify the redshift-space distortion effect, we focus mainlyon 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 thecross-covariance between the power and bispectra, and the auto-covariance ofthe bispectrum in redshift space. We test the validity of our calculations bycomparing them with the covariance matrices measured from the MultiDark-Patchymock catalogues that are designed to reproduce the galaxy clustering measuredfrom the Baryon Oscillation Spectroscopic Survey Data Release 12. We argue thatthe simple, leading-order perturbation theory works because the shot-noisecorrections for the Patchy mocks are more dominant than other higher-orderterms we ignore. In the meantime, we confirm some discrepancies in thecomparison, especially of the cross-covariance. We discuss potential sources ofsuch discrepancies. We also show that our PT model reproduces well thecumulative signal-to-noise of the power spectrum and the bispectrum as afunction of maximum wavenumber, implying that our PT model capturessuccessfully essential contributions to the covariance matrices.

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