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The measurement of the abundance of galaxy clusters in the Universe is asensitive probe of cosmology, which depends on both the expansion history ofthe Universe and the growth of structure. Density fluctuations across thefinite survey volume add noise to this measurement, this is often referred toas super-sample covariance (SSC). For an unbinned cluster analysis, such noisehas not been included in the cluster likelihood, since the effect of SSC wassmall compared to the Poisson shot-noise for samples of a few hundred clusters.For upcoming large cluster surveys such as the Rubin LSST, which will delivercatalogs of tens of thousands of clusters, this effect will no longer benegligible. In this paper, we propose a new hybrid likelihood based on theGauss-Poisson Compound model (GPC), by using infinitesimal mass bins andstandard redshift bins. This likelihood has the advantages of an unbinnedPoisson likelihood whilst successfully incorporating the effects of SSC. Usinga simulated dark matter halo catalog, we find that the hybrid likelihood,accounting for both Poisson noise and SSC, increases the dispersion of theparameter posteriors by 20 percent when using 100,000 clusters compared to thestandard unbinned likelihood, based on Poisson statistics only.

Towards including super-sample covariance in the unbinned likelihood for cluster abundance cosmology