Cluster abundance cosmology: Towards including Super-Sample Covariance in the unbinned likelihood

Abstract

International audienceThe measure of the abundance of galaxy clusters in the Universe is a sensitive probe of cosmology, sensitive to both the expansion history and the growth of structure. Density fluctuations across the finite survey volume induce noise to this measure, often referred to as Super-Sample Covariance (SSC). In the past for unbinned cluster analysis such noise has not been included in the cluster likelihood. In this paper, we present a derivation of the unbinned likelihood accounting for Super-Sample Covariance by using a Gauss-Poisson Compound (GPC) likelihood. We show that deriving the unbinned likelihood with SSC from the expansion of the GPC formalism to the second order in density perturbation is not sufficient, preventing us from using analytical methods already explored in the literature. In order to solve this issue, we still used the GPC model to derive an alternative "hybrid" likelihood, by using standard redshift bins. Using simulated dark matter halo catalog obtained by the PINOCCHIO algorithm, we found that the hybrid likelihood, accounting for both Poisson noise and SSC, increases the dispersion of the parameter posteriors by 25 per cent using 2,500 clusters, compared to the standard Poisson likelihood