We validate the COVMOS method introduced in our previous study allowing for the fast simulation of catalogues of different cosmological field tracers (e.g. dark matter particles, halos, galaxies, etc.). The power spectrum and one-point probability distribution function of the underlying tracer's density field are set as inputs of the method and arbitrarily chosen by the user. To evaluate the validity domain of COVMOS at the level of the produced two-point statistics covariance matrix, we chose to target these two input statistical quantities from realistic N-body simulation outputs. We performed this cloning procedure based on the ΛCDM as well as on a massive neutrino cosmology, for five redshifts in the range of z ∈ [0, 2]. First, we validated the output real-space two-point statistics (both in the configuration and Fourier space) and estimated over 5, 000 COVMOS realisations per redshift and per cosmology, with a volume of 1 [Gpc/h] 3 and 10 8 particles each. This validation was performed against the corresponding N-body measurements, estimated from 50 simulations. We found the method to be valid up to k ∼ 0.2h/Mpc for the power spectrum and down to r ∼ 20 Mpc/h for the correlation function. Then, we extended the method by proposing a new modelling of the peculiar velocity distribution, aimed at reproducing the redshift-space distortions both in the linear and mildly non-linear regimes. After validating this prescription, we finally compared and validated the resulting redshift-space two-point statistics covariance matrices in the same range of scales. We released the Python code associated with this method on a public repository, which allows for the production of tens of thousands of realisations in record time. In particular, COVMOS is intended for any study involving large-scale galaxy-survey science that requires a large number of mock realisations.

Super-sample covariance (SSC) is an important effect for cosmological analyses that use the deep structure of the cosmic web; it may, however, be nontrivial to include it practically in a pipeline. We solve this difficulty by presenting a formula for the precision (inverse covariance) matrix and show applications to update likelihood or Fisher forecast pipelines. The formula has several advantages in terms of speed, reliability, stability, and ease of implementation. We present an analytical application to show the formal equivalence between three approaches to SSC: (i) at the usual covariance level, (ii) at the likelihood level, and (iii) with a quadratic estimator. We then present an application of this computationally efficient framework for studying the impact of inaccurate modelling of SSC responses for cosmological constraints from stage IV surveys. We find that a weak-lensing-only analysis is very sensitive to inaccurate modelling of the scale dependence of the response, which needs to be calibrated at the ∼15% level. The sensitivity to this scale dependence is less severe for the joint weak-lensing and galaxy clustering analysis (also known as 3×2pt). Nevertheless, we find that both the amplitude and scale-dependence of the responses have to be calibrated at better than 30%.