Preparation for the analysis and interpretation of Euclid galaxy clusters

Euclid is a Medium Class satellite mission to be launched by ESA in 2023. The Euclid satellite is mainly devoted to cosmology and intends to unveil the nature of the Dark Energy and the Dark Matter by using cosmological probes such as galaxy clusters. Euclid is composed of two instruments: the Visible (VIS) instrument and the Near Infrared Spectrometer and Photometer (NISP). This thesis is focused, first, in the characterization of the Euclid infrared detectors of the NISP instrument, and second, the construction of a synthetic catalogue for computing the selection function, essential for using galaxy clusters as cosmological probes. The first part of the thesis includes the context of the thesis, form the standard cosmological model to galaxy clusters as cosmological probes and their observational signatures in the optical and infrared wavelengths, and how to detect them, passing through an historical context of numerical simulations in cosmology. In the second part we introduce the Euclid satellite and we estimate the implications of correlated readout noise in the NISP detectors for the final in-flight flux measurements. We conclude that the final bias on the in-flight NISP flux measurements should still be negligible even in the white noise approximation, which is taken as a baseline for the Euclid on-board processing. The third part introduces two properties of galaxy clusters in the optical/infrared domain, fundamental for its detection: the luminosity function (LF) and the cluster galaxy density distribution. These properties are measured from the Euclid Mock catalogue and we reproduce them by fitting two analytical models over the full redshift and mass range of Euclid: the Schechter and the Navarro-Frenk-White (NFW) models. In the forth part of the thesis we present the same observational properties as in the third part but for hydrodynamical simulations, done in the framework of the 300. Project. Due to resolution problems in the computation of the luminosity function, we study the resolution effects in the galaxy density property for being able to simulate a more realistic cluster galaxy members distribution, this time by using an analytical Einasto profile. The last part of the thesis is dedicated to the construction of a synthetic catalogue from the analytical properties of the Euclid mock catalogue. Then we inject this cluster galaxy members catalogue into the Euclid one and we ran an identification algorithm to detect cluster, for later on computing the completeness and purity. (author)