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Fast computation of non-Gaussian covariance of redshift-space galaxy power spectrum multipoles. (arXiv:2308.08593v1 [astro-ph.CO])

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The non-Gaussian part of the covariance matrix of the galaxy power spectrum
involves the connected four-point correlation in Fourier space, i.e.
trispectrum. This paper introduces a fast method to compute the non-Gaussian
part of the covariance matrix of the galaxy power spectrum multipoles in
redshift space at tree-level standard perturbation theory. For the tree-level
galaxy trispectrum, the angular integral between two wavevectors can be
evaluated analytically by employing an FFTLog. The new implementation computes
the non-Gaussian covariance of the power spectrum monopole, quadrupole,
hexadecapole and their cross-covariance in O(10) seconds, for an effectively
arbitrary number of instances of cosmological and galaxy bias parameters and
redshift, without any parallelization or acceleration. It is a large advantage
over conventional numerical integration. We demonstrate that the computation of
the covariance at k = 0.005 - 0.4 h/Mpc gives results with 0.1 - 1% accuracy.
The efficient computation of the analytic covariance can be useful for future
galaxy surveys, especially utilizing multi-tracer analysis.

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