Covariance of the matter power spectrum including the survey window function effect: N-body simulations vs. fifth-order perturbation theory on grid

TL;DR

This paper develops a fifth-order perturbation theory method to accurately compute the covariance matrix of the matter power spectrum, including survey window effects, and validates it against N-body simulations.

Contribution

It introduces a fast grid-based fifth-order perturbation theory approach (GridSPT) to estimate the covariance matrix with survey window effects, matching N-body simulation results.

Findings

NNLO GridSPT reproduces N-body covariance on quasi-linear scales.

Inclusion of survey window effects improves covariance matrix accuracy.

The method avoids explicit trispectrum computation.

Abstract

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 quasi-linear 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.