We studied the imprints that feedback from Active Galactic Nuclei (AGN) leaves on the intracluster plasma during the assembly history of galaxy clusters. To this purpose we used state-of-the-art cosmological hydrodynamical simulations based on an updated version of the Tree-PM SPH GADGET-3 code, comparing three sets of simulations with different prescriptions for the physics of baryons (including AGN and/or stellar feedback). We explore the effect of these different physics, in particular AGN feedback, on IntraCluster medium (ICM) properties observed via Sunyaev-Zel’dovich (SZ) effect using an extended set of galaxy clusters (~100 clusters with M500 masses above 5 × 1013M⊙/h). Some of the main findings are that the scaling relation between the integrated SZ flux and the galaxy cluster total mass is in good accordance with several observed samples, especially for massive clusters, and does not show any clear redshift evolution, with the slope of the relation close to the theoretical one in the AGN feedback case. As for the scatter of this relation, we obtain a mild dependence on the cluster dynamical state.

Comparisons between observed and predicted strong lensing properties of galaxy clusters have been used to claim either tension or consistency with ΛCDM cosmology. However, standard approaches to such tests are unable to quantify the preference for one cosmology over another. We advocate a Bayesian approach whereby the parameters defining the scaling relation between Einstein radii and cluster mass are treated as the observables. We demonstrate a method of estimating the likelihood for observing these parameters under the ΛCDM framework, using the X-ray selected z > 0.5 MACS clusters as a case in point and employing both N-body and hydrodynamic simulations of clusters. We account for cluster lens triaxiality within the modelling of the likelihood function. Cluster selection criteria is found to play as important a role as the uncertainty related to the description of star formation and feedback.

I review the current status of the comparison between observational properties of galaxy clusters and predictions from cosmological hydrodynamical simulations. My presentation focuses on the thermodynamical and chemical properties of the intra–cluster medium (ICM), as observed in the X–ray band. I finally discuss the properties of the galaxy population and their relation with the those of the hot diffuse gas. The emerging picture highlights that the current numerical description of galaxy clusters is able to account for several properties, such as the slope of the temperature profiles outside the core regions, the global chemical enrichment of the ICM and the color and luminosities for the bulk of the galaxy population. However, important discrepancies between observations and simulations are found, such as the thermal structure of cool cores and the colors of the brightest cluster galaxies. I emphasize that such two failures are two faces of the same problem, namely the difficulty of regulating gas cooling and star formation inside the most massive dark matter halos. This calls for the need of a source of energy feedback, which is not directly related to star formation, thus pointing towards AGN as a natural candidate for such a mechanism.

We have developed in GADGET-2 a feature–rich and highly flexible code for modeling the stellar evolution and the chemical enrichment. Simulating clusters, we find a very good agreement in reproducing both the radial abundance profiles and the enrichment history of the Intra–Cluster medium.

We examine the systematics affecting the X-ray mass estimators applied toChandra-like long exposures images of five simulated clusters.

The combination of the collecting power of an ELT with an ultra-stable high resolution spectrograph opens up the possibility to measure for the first time directly the dynamical effect of the acceleration of the Universe. CODEX will also provide unique opportunities for advance in many other branches of astrophysics. The CODEX design is based on an array of several identical spectrographs. It is highly modular and can be easily adapted to a large range of sky apertures and telescope diameters. CODEX is designed to work as a seeing limited instrument. The requirements for the telescope are moderate and clearly identified.