Non-Gaussian Error Contribution to Likelihood Analysis of the Matter Power Spectrum

TL;DR

This paper investigates the impact of non-Gaussian errors on the likelihood analysis of the matter power spectrum, revealing their significant effect on parameter errors and biases, and comparing simulation results with Fisher matrix predictions.

Contribution

It provides a detailed analysis of non-Gaussian error contributions using extensive N-body simulations and compares these with Fisher matrix forecasts for the matter power spectrum.

Findings

Non-Gaussian errors can increase parameter errors by up to a factor of 5 for single-parameter fits.

Degeneracies in multi-parameter fits mitigate the impact of non-Gaussian errors.

Biases due to non-Gaussian errors are smaller than 1 sigma statistical errors.

Abstract

We study the sample variance of the matter power spectrum for the standard Lambda Cold Dark Matter universe. We use a total of 5000 cosmological N-body simulations to study in detail the distribution of best-fit cosmological parameters and the baryon acoustic peak positions. The obtained distribution is compared with the results from the Fisher matrix analysis with and without including non-Gaussian errors. For the Fisher matrix analysis, we compute the derivatives of the matter power spectrum with respect to cosmological parameters using directly full nonlinear simulations. We show that the non-Gaussian errors increase the unmarginalized errors by up to a factor 5 for k_{max}=0.4h/Mpc if there is only one free parameter provided other parameters are well determined by external information. On the other hand, for multi-parameter fitting, the impact of the non-Gaussian errors is significantly mitigated due to severe parameter degeneracies in the power spectrum. The distribution of the acoustic peak positions is well described by a Gaussian distribution, with its width being consistent with the statistical interval predicted from the Fisher matrix. We also examine systematic bias in the best-fit parameter due to the non-Gaussian errors. The bias is found to be smaller than the 1 sigma statistical error for both the cosmological parameters and the acoustic scale positions.