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