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We present a Next-to-next-to-leading (fifth or NNLO) order calculation forthe covariance matrix of the matter power spectrum, taking into account theeffect of survey window functions. Using the grid-based calculation scheme forthe standard perturbation theory, GridSPT, we quickly generate multiplerealizations of the nonlinear density fields to fifth order in perturbationtheory, then estimate the power spectrum and the covariance matrix from thesample. To the end, we have obtained the non-Gaussian covariance originatedfrom the one-loop trispectrum without explicitly computing the trispectrum. Bycomparing the GridSPT calculations with the N-body results, we show that NNLOGridSPT result reproduces the N-body results on quasi-linear scales where SPTaccurately models nonlinear matter power spectrum. Incorporating the surveywindow function effect to GridSPT is rather straightforward, and the resultingNNLO covariance matrix also matches well with the N-body results.

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