Euclid: Effect of sample covariance on the number counts of galaxy clusters

Fumagalli, A. et al. Euclid Consortium
[Aims] We investigate the contribution of shot-noise and sample variance to uncertainties in the cosmological parameter constraints inferred from cluster number counts, in the context of the Euclid survey.
[Methods] By analysing 1000 Euclid-like light cones, produced with the PINOCCHIO approximate method, we validated the analytical model of Hu & Kravtsov (2003, ApJ, 584, 702) for the covariance matrix, which takes into account both sources of statistical error. Then, we used such a covariance to define the likelihood function that is better equipped to extract cosmological information from cluster number counts at the level of precision that will be reached by the future Euclid photometric catalogs of galaxy clusters. We also studied the impact of the cosmology dependence of the covariance matrix on the parameter constraints.
[Results] The analytical covariance matrix reproduces the variance measured from simulations within the 10 percent; such a difference has no sizeable effect on the error of cosmological parameter constraints at this level of statistics. Also, we find that the Gaussian likelihood with full covariance is the only model that provides an unbiased inference of cosmological parameters without underestimating the errors, and that the cosmology-dependence of the covariance must be taken into account.
SB, AS and AF acknowledge financial support from the ERC-StG ‘ClustersxCosmo’ grant agreement 716762, the PRIN-MIUR 2015W7KAWC grant, the ASI-Euclid contract and the INDARK grant. TC is supported by the INFN INDARK PD51 grant and by the PRIN-MIUR 2015W7KAWC grant. Our analyses have been carried out at: CINECA, with the projects INA17_C5B32 and IsC82_CosmGC; the computing center of INAF-Osservatorio Astronomico di Trieste, under the coordination of the CHIPP project (Bertocco et al. 2019; Taffoni et al. 2020). The Euclid Consortium acknowledges the European Space Agency and a number of agencies and institutes that have supported the development of Euclid, in particular the Academy of Finland, the Agenzia Spaziale Italiana, the Belgian Science Policy, the Canadian Euclid Consortium, the Centre National d’Etudes Spatiales, the Deutsches Zentrum für Luft- und Raumfahrt, the Danish Space Research Institute, the Fundação para a Ciência e a Tecnologia, the Ministerio de Economia y Competitividad, the National Aeronautics and Space Administration, the Netherlandse Onderzoekschool Voor Astronomie, the Norwegian Space Agency, the Romanian Space Agency, the State Secretariat for Education, Research and Innovation (SERI) at the Swiss Space Office (SSO), and the United Kingdom Space Agency. A complete and detailed list is available on the Euclid website (http://www.euclid-ec.org).