Euclid: Modelling observational effects in cluster counts and cluster clustering

This study explores the impact of observational and modelling systematic e ffects on cluster number counts and cluster clustering and provides model prescriptions for their joint analysis in the context of the Euclid survey. Using 1000 Euclid-like cluster catalogues, we investigated the e ffect of systematic uncertainties on cluster summary statistics and their auto- and cross-covariance, and performed a likelihood analysis to evaluate their impact on cosmological constraints, with a focus on the matter density parameter (Omega(m)) and on the power spectrum amplitude (sigma(8)). Combining cluster clustering with number counts significantly improves cosmological constraints, with the figure of merit increasing by over 300% compared to number counts alone. We confirm that the two probes are uncorrelated, and the cosmological constraints derived from their combination are almost insensitive to the cosmology dependence of the covariance. We find that photometric redshift uncertainties broaden cosmological posteriors by 20-30%, while secondary e ffects such as redshift-space distortions (RSDs) have a smaller impact on the posteriors - 5% for clustering alone, 10% when combining probes - but can significantly bias the constraints if neglected. We show that clustering data below 60 h(-1) Mpc provides additional constraining power, while scales larger than the acoustic oscillation scale add almost no information on Omega(m) and sigma(8) parameters. The RSDs and photo-z uncertainties also influence the number count covariance, with a significant impact of about 15-20% on the parameter constraints.