Testing the accuracy of likelihoods for cluster abundance cosmology

Abstract

The abundance of galaxy clusters is a sensitive probe to the amplitude of matter density fluctuations, the total amount of matter in the Universe as well as its expansion history. Inferring correct values and accurate uncertainties of cosmological parameters requires accurate knowledge of cluster abundance statistics, encoded in the likelihood function. In this paper, we test the accuracy of cluster abundance likelihoods used in the literature, namely the Poisson and Gaussian likelihoods as well as the more complete description of the Gauss-Poisson Compound likelihood. This is repeated for a variety of binning choices and analysis setups. In order to evaluate the accuracy of a given likelihood, this work compares individual posterior covariances to the covariance of estimators over the 1000 simulated dark matter halo catalogs obtained from PINOCCHIO algorithm. We find that for Rubin/LSST or Euclid-like surveys the Gaussian likelihood gives robust constraints over a large range of binning choices. The Poisson likelihood, that does not account for sample covariance, always underestimates the errors on the parameters, even when the sample volume is reduced or only high-mass clusters are considered. We find no benefit in using the more complex Gauss-Poisson Compound likelihood as it gives essentially the same results as the Gaussian likelihood, but at a greater computational cost. Finally, in this ideal setup, we note only a small gain on the parameter error bars when using a large number of bins in the mass-redshift plane.

13 pages, 10 figures, accepted for publication in MNRAS

References in corpus (10)

• Weighing the Giants IV: Cosmology and Neutrino Mass
• Constraining the Scatter in the Mass-Richness Relation of maxBCG Clusters With Weak Lensing and X-ray Data
• The impact of baryons on massive galaxy clusters: halo structure and cluster mass estimates
• On the insufficiency of arbitrarily precise covariance matrices: non-Gaussian weak lensing likelihoods
• Quantifying lost information due to covariance matrix estimation in parameter inference
• AMICO galaxy clusters in KiDS-DR3: Constraints on cosmological parameters and on the normalisation of the mass-richness relation from clustering
• Euclid: Effect of sample covariance on the number counts of galaxy clusters
• Generalised Fisher Matrices
• Impact of survey geometry and super-sample covariance on future photometric galaxy surveys
• Measuring weak lensing masses on individual clusters

Cited by in corpus (4)

• Cosmological constraints from abundance, weak-lensing and clustering of galaxy clusters: application to the SDSS
• Cosmological inference including massive neutrinos from the matter power spectrum: biases induced by uncertainties in the covariance matrix
• Euclid: Exploring observational systematics in cluster cosmology -- a comprehensive analysis of cluster counts and clustering
• Towards including super-sample covariance in the unbinned likelihood for cluster abundance cosmology