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Future galaxy surveys will provide accurate measurements of the matter powerspectrum across an unprecedented range of scales and redshifts. The analysis ofthese data will require one to accurately model the imprint of non-linearitiesof the matter density field. In particular, these induce a non-Gaussiancontribution to the data covariance that needs to be properly taken intoaccount to realise unbiased cosmological parameter inference analyses. Here, westudy the cosmological dependence of the matter power spectrum covariance usinga dedicated suite of N-body simulations, the Dark Energy Universe Simulation -Parallel Universe Runs (DEUS-PUR) {\it Cosmo}. These consist of 512realizations for 10 different cosmologies where we vary the matter density$\Omega_m$, the amplitude of density fluctuations $\sigma_8$, the reducedHubble parameter $h$ and a constant dark energy equation of state $w$ byapproximately $10\%$. We use these data to evaluate the first and secondderivatives 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. By performinga Fisher matrix analysis we explore the impact of different choices inmodelling the cosmological dependence of the covariance. Our results suggestthat fixing the covariance to a fiducial cosmology can significantly affect therecovered parameter errors and that modelling the cosmological dependence ofthe variance while keeping the correlation coefficient fixed can alleviate theimpact of this effect.

Cosmological Model Parameter Dependence of the Matter Power Spectrum Covariance from the DEUS-PUR $Cosmo$ Simulations