2020/07/31 by Atsushi Taruya, Takahiro Nishimichi, Donghui Jeong
Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Cosmology and Gravitation Theories #Covariance #Covariance function #Covariance intersection #Covariance matrix #Galaxies: Formation, Evolution, Phenomena #Gaussian #Mathematics #Matérn covariance function #Perturbation (astronomy) #Perturbation theory (quantum mechanics) #Physics #Quantum mechanics #Spectral density #Statistics #Stellar, planetary, and galactic studies #Trispectrum #astro-ph.CO
paper · pdf · doi:10.1103/physrevd.103.023501
published as Phys. Rev. D 103, 023501 (2021) · 20 pages, 16 figures, updated to match the version published in PRD
openalex created_date 2020/07/16 · openalex publication_date 2021/01/05 · arxiv created 2021/01/06 · arxiv updated 2021/01/13 · openalex updated_date 2026/08/06
We present a next-to-next-to-leading (fifth or NNLO) order calculation for the covariance matrix of the matter power spectrum, taking into account the effect of survey window functions. Using the grid-based calculation scheme for the standard perturbation theory, GridSPT, we quickly generate multiple realizations of the nonlinear density fields to fifth order in perturbation theory, then estimate the power spectrum and the covariance matrix from the sample. To the end, we have obtained the non-Gaussian covariance originated from the one-loop trispectrum without explicitly computing the trispectrum. By comparing the GridSPT calculations with the N-body results, we show that NNLO GridSPT result reproduces the N-body results on quasilinear scales, where SPT accurately models nonlinear matter power spectrum. Incorporating the survey window function effect to GridSPT is rather straightforward, and the resulting NNLO covariance matrix also matches well with the N-body results.