Cosmology with galaxy clusters

Clusters of galaxies are powerful probes to constrain parameters that describe the cosmological models and to distinguish among different models. Since, the evolution of the cluster mass function and large-scale clustering contain the informations about the linear growth rate of perturbations and the expansion history of the Universe, clusters have played an important role in establishing the current cosmological paradigm. It is crucial to know how to determine the cluster mass from observational quantities when using clusters as cosmological tools. For this, numerical simulations are helpful to define and study robust cluster mass proxies that have minimal and well understood scatter across the mass and redshift ranges of interest. Additionally, the bias in cluster mass determination can be constrained via observations of the strong and weak lensing effect, X-ray emission, the Sunyaev- Zel’dovic effect, and the dynamics of galaxies.A major advantage of X-ray surveys is that the observable-mass relation is tight. Moreover, clusters can be easily identified in X-ray as continuous, extended sources. As of today, interesting cosmological constraints have been obtained from relatively small cluster samples (~10²), X-ray selected by the ROSAT satellite over a wide redshift range (0<z<0.8), and with robust mass estimates obtained with Chandra and XMM follow-up. These constraints complement those from CMB and SNIa observations. Moreover, the large-scale power spectrum has been constructed using a low redshift (z<0.2) sample of ~10³ nearby clusters, the ROSAT All-Sky Survey.The next generation of X-ray telescopes will enhance the statistics of detected clusters and enlarge their redshift coverage. In particular, eROSITA will produce a catalog of >10⁵ clusters with photometric redshifts from multi-band optical surveys (e.g. PanSTARRS, DES, and LSST). This will vastly improve upon current cosmological constraints, especially by the synergy with other cluster surveys that have been or will be performed at other wavelengths (such as DES, Euclid, Planck, SPT, and SKA). To fully exploit such a large amount of data, it will become fundamental to understand the effects of baryonic physics and to improve the precision of the theoretical mass function at the high mass end using numerical simulations.