Euclid: Modelling observational effects in cluster counts and cluster clustering

This study explores the impact of observational and modelling systematic effects 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 effect 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 (om) and on the power spectrum amplitude (σ_8). -1 ,Mpc provides additional constraining power, while scales larger than the acoustic oscillation scale add almost no information on om and σ_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.