Perturbation theory approach to predict the covariance matrices of the galaxy power spectrum and bispectrum in redshift space. (arXiv:1908.06234v1 [astro-ph.CO])
<a href="http://arxiv.org/find/astro-ph/1/au:+Sugiyama_N/0/1/0/all/0/1">Naonori S. Sugiyama</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Saito_S/0/1/0/all/0/1">Shun Saito</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Beutler_F/0/1/0/all/0/1">Florian Beutler</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Seo_H/0/1/0/all/0/1">Hee-Jong Seo</a>
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 $ksim0.2hk$,
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.
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 $ksim0.2hk$,
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.
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