Simulations of Baryon Acoustic Oscillations II: Covariance matrix of the matter power spectrum

TL;DR

This study uses extensive N-body simulations to analyze the non-Gaussian errors in the matter power spectrum, revealing their significant impact on signal-to-noise ratios and cosmological parameter estimation, especially at BAO scales.

Contribution

It provides a detailed quantification of non-Gaussian errors in the matter power spectrum and their effects on cosmological measurements using large-scale simulations.

Findings

Non-Gaussian errors can reduce S/N ratios by up to a factor of 4.

Power spectrum estimators at BAO scales are well approximated by Gaussian distributions.

Survey volume and shot noise further degrade the cosmological information content.

Abstract

We use 5000 cosmological N-body simulations of 1(Gpc/h)^3 box for the concordance LCDM model in order to study the sampling variances of nonlinear matter power spectrum. We show that the non-Gaussian errors can be important even on large length scales relevant for baryon acoustic oscillations (BAO). Our findings are (1) the non-Gaussian errors degrade the cumulative signal-to-noise ratios (S/N) for the power spectrum amplitude by up to a factor of 2 and 4 for redshifts z=1 and 0, respectively. (2) There is little information on the power spectrum amplitudes in the quasi-nonlinear regime, confirming the previous results. (3) The distribution of power spectrum estimators at BAO scales, among the realizations, is well approximated by a Gaussian distribution with variance that is given by the diagonal covariance component. (4) For the redshift-space power spectrum, the degradation in S/N by non-Gaussian errors is mitigated due to nonlinear redshift distortions. (5) For an actual galaxy survey, the additional shot noise contamination compromises the cosmological information inherent in the galaxy power spectrum, but also mitigates the impact of non-Gaussian errors. The S/N is degraded by up to 30% for a WFMOS-type survey. (6) The finite survey volume causes additional non-Gaussian errors via the correlations of long-wavelength fluctuations with the fluctuations we want to measure, further degrading the S/N values by about 30% even at high redshift z=3.