Non-linear matter power spectrum covariance matrix errors and cosmological parameter uncertainties - Blot, Linda; Amendola, Luca (Monthly notices of the Royal Astronomical Society, 2016)
The covariance of the matter power spectrum is a key element of the analysis of galaxy clustering data. Independent realizations of observational measurements can be used to sample the covariance, nevertheless statistical sampling errors will propagate into the cosmological parameter inference potentially limiting the capabilities of the upcoming generation of galaxy surveys. The impact of these errors as function of the number of realizations has been previously evaluated for Gaussian distributed data. However, non-linearities in the late-time clustering of matter cause departures from Gaussian statistics. Here, we address the impact of non-Gaussian errors on the sample covariance and precision matrix errors using a large ensemble of N-body simulations. In the range of modes where finite volume effects are negligible (0.1 ≲ k [h Mpc−1] ≲ 1.2), we find deviations of the variance of the sample covariance with respect to Gaussian predictions above ∼10 per cent at k > 0.3 h Mpc−1. Over the entire range these reduce to about ∼5 per cent for the precision matrix. Finally, we perform a Fisher analysis to estimate the effect of covariance errors on the cosmological parameter constraints. In particular, assuming Euclid-like survey characteristics we find that a number of independent realizations larger than 5000 is necessary to reduce the contribution of sampling errors to the cosmological parameter uncertainties at subpercent level. We also show that restricting the analysis to large scales k ≲ 0.2 h Mpc−1 results in a considerable loss in constraining power, while using the linear covariance to include smaller scales leads to an underestimation of the errors on the cosmological parameters.