Cosmology with clusters of galaxies

Clusters of galaxies occupy a special place in the hierarchy of cosmic structures. They arise from the collapse of initial perturbations having a typical comoving scale of about 10 hMpc. According to the standard model of cosmic structure formation, the Universe is dominated by gravitational dynamics in the linear or weakly non–linear regime and on scales larger than this. In this case, the description of cosmic structure formation is relatively simple since gas dynamical effects are thought to play a minor role, while the dominating gravitational dynamics still preserves memory of initial conditions. On smaller scales, instead, the complex astrophysical processes, related to galaxy formation and evolution, become relevant. Gas cooling, star formation, feedback from supernovae (SN) and active galactic nuclei (AGN) significantly change the evolution of cosmic baryons and, therefore, the observational properties of the structures. Since clusters of galaxies mark the transition between these two regimes, they have been studied for decades both as cosmological tools and as astrophysical laboratories. In this Chapter I concentrate on the role that clusters play in cosmology. I will highlight that, in order for them to be calibrated as cosmological tools, one needs to understand in detail the astrophysical processes which determine their observational characteristics, i.e. the properties of the cluster galaxy population and those of the diffuse intra–cluster medium (ICM). Constraints of cosmological parameters using galaxy clusters have been placed so far by applying a variety of methods. For example: