If at First You Don't Succeed, Trispectrum: I. Estimating the Matter Power Spectrum Covariance with Higher-Order Statistics

TL;DR

This paper introduces a method to estimate non-Gaussian matter power spectrum covariance matrices directly from higher-order statistics, reducing simulation requirements and enabling covariance inference from survey data.

Contribution

The authors derive estimators for the full non-Gaussian covariance, including super-sample effects, using bispectrum and trispectrum measurements, demonstrated on simulations.

Findings

Achieved unbiased covariance estimates at percent accuracy with only 25 simulations.

Reduced the number of simulations needed compared to traditional sample covariance estimates.

Enabled potential inference of covariance matrices directly from survey data.

Abstract

We present a method to estimate non-Gaussian power spectrum covariance matrices by directly measuring the response of the small-scale power spectrum to long-wavelength perturbations via bispectrum and trispectrum estimators. Specifically, we derive estimators for the complete non-Gaussian matter power spectrum covariance, including the super-sample contribution, in terms of the squeezed bispectrum and collapsed trispectrum of the underlying density field. We apply these estimators to the Quijote simulations, and recover unbiased estimates of the small-scale ($k\gtrsim 0.15~h/{\rm Mpc}$) matter power spectrum covariance at the percent level using only 25 simulations - comparable to the precision of the sample covariance estimated using 5,000 simulations. This technique significantly reduces the number of simulations needed to estimate power spectrum covariances and opens the possibility of inferring power spectrum covariances directly from survey data, enabling stringent tests of simulations and, potentially, power spectrum analyses that do not rely on external covariance matrices.