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We present here the cosmo-SLICS, a new suite of simulations speciallydesigned for the analysis of current and upcoming weak lensing data beyond thestandard two-point cosmic shear. We sample the $[\Omega_{\rm m}, \sigma_8, h,w_0]$ parameter space at 25 points organised in a Latin hyper-cube, spanning arange that contains most of the $2\sigma$ posterior distribution from ongoinglensing surveys. At each of these nodes we evolve a pair of $N$-bodysimulations in which the sampling variance is highly suppressed, and ray-tracethe volumes 800 times to further increase the effective sky coverage. Weextract a lensing covariance matrix from these pseudo-independent light-conesand show that it closely matches a brute-force construction based on anensemble of 800 truly independent $N$-body runs. More precisely, a Fisheranalysis reveals that both methods yield marginalized two-dimensionalconstraints that vary by less than 6% in area, a result that holds underdifferent survey specifications and that matches to within 15% the areaobtained from an analytical covariance calculation. Extending this comparisonwith our 25 $w$CDM models, we probe the cosmology dependence of the lensingcovariance directly from numerical simulations, reproducing remarkably well theFisher results from the analytical models at most cosmologies. We demonstratethat varying the cosmology at which the covariance matrix is evaluated in thefirst place might have an order of magnitude greater impact on the parameterconstraints than varying the choice of covariance estimation technique. Wepresent a test case in which we generate fast predictions for both the lensingsignal and its associated variance with a flexible Gaussian process regressionemulator, achieving an accuracy of a few percent on the former and 10% on thelatter.

Cosmic Shear Covariance Matrix in $w$CDM: Cosmology Matters