The Impact of Non-Gaussianity upon Cosmological Forecasts

TL;DR

This paper demonstrates that assuming Gaussian statistics in 3D galaxy survey forecasts significantly overestimates parameter constraints, especially for dark energy, highlighting the importance of accounting for non-Gaussian effects in non-linear regimes.

Contribution

It provides an analytic approach to quantify non-Gaussian effects on cosmological parameter forecasts, revealing substantial overestimations when Gaussian assumptions are used.

Findings

Gaussian assumptions overestimate information by up to an order of magnitude.

Non-Gaussian effects mainly impact amplitude-like parameters after marginalization.

Dark energy parameter errors are underestimated by over 50% under Gaussian assumptions.

Abstract

The primary science driver for 3D galaxy surveys is their potential to constrain cosmological parameters. Forecasts of these surveys' effectiveness typically assume Gaussian statistics for the underlying matter density, despite the fact that the actual distribution is decidedly non-Gaussian. To quantify the effect of this assumption, we employ an analytic expression for the power spectrum covariance matrix to calculate the Fisher information for BAO-type model surveys. We find that for typical number densities, at $k_\mathrm{max} = 0.5 h$ Mpc$^{-1}$, Gaussian assumptions significantly overestimate the information on all parameters considered, in some cases by up to an order of magnitude. However, after marginalizing over a six-parameter set, the form of the covariance matrix (dictated by $N$-body simulations) causes the majority of the effect to shift to the "amplitude-like" parameters, leaving the others virtually unaffected. We find that Gaussian assumptions at such wavenumbers can underestimate the dark energy parameter errors by well over 50 per cent, producing dark energy figures of merit almost 3 times too large. Thus, for 3D galaxy surveys probing the non-linear regime, proper consideration of non-Gaussian effects is essential.