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

• Published in: Monthly notices of the Royal Astronomical Society Vol. 497; no. 2; pp. 1684 - 1711
• Main Authors: Sugiyama, Naonori S, Saito, Shun, Beutler, Florian, Seo, Hee-Jong
• Format: Journal Article
• Language: English
• Published: United States Oxford University Press 01-09-2020; Royal Astronomical Society
• Subjects: ASTRONOMY AND ASTROPHYSICS; cosmology: dark matter; cosmology: large-scale structure of Universe; cosmology: observations; cosmology: theory; cosmology: large-scale structure of Universe; cosmology: observations; cosmology: theory; cosmology: dark matter
• ISSN: 0035-8711; 1365-2966
• DOI: 10.1093/mnras/staa1940

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 autocovariance 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 PT 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 ratio 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.