Cosmological model parameter dependence of the matter power spectrum covariance from the DEUS-PUR Cosmo simulations

Future galaxy surveys will provide accurate measurements of the matter power spectrum across an unprecedented range of scales and redshifts. The analysis of these data will require to accurately model the imprint of non-linearities on the matter density field, which induces a non-Gaussian contribution to the data covariance. As the imprint of non-linearities is cosmology dependent, a further complication arises from accounting for the cosmological dependence of the non-Gaussian part of the covariance. Here, we study this using a dedicated suite of N-body simulations, the Dark Energy Universe Simulation - Parallel Universe Runs (DEUS-PUR) $Cosmo$. These consist of 512 realizations for 10 different cosmologies where we vary the matter density $\Omega_m$, the amplitude of density fluctuations $\sigma_8$, the reduced Hubble parameter $h$ and a constant dark energy equation of state $w$ by approximately $10\%$. We use these data to evaluate the first and second derivatives of the power spectrum covariance with respect to a fiducial $\Lambda$CDM cosmology. We find that the variations can be as large as $150\%$ depending on the scale, redshift and model parameter considered. Using a Fisher matrix approach, we evaluate the impact of using a covariance estimated at a fiducial model rather than the true underlying cosmology. We find that the estimated $1\sigma$ errors are affected at approximately $5\%$, $20\%$, $50\%$ and $120\%$ level when assuming non-fiducial values of $h$, $w$, $\Omega_m$ and $\sigma_8$ respectively. These results suggest that the use of cosmology-dependent covariances is key for precision cosmology.