Hydrodynamical simulations of galaxy clusters in dark energy cosmologies

In this work we investigate the influence of dark energy on structure formation, within five different cosmological models, namely a concordance $\Lambda$CDM model, two models with dynamical dark energy, viewed as a quintessence scalar field (using a RP and a SUGRA potential form) and two extended quintessence models (EQp and EQn) where the quintessence scalar field interacts non-minimally with gravity (scalar-tensor theories). We adopted for all models the normalization of the matter power spectrum $\sigma_{8}$ to match the CMB data. For each model, we perform hydrodynamical simulations in a cosmological box of $(300 \ {\rm{Mpc}} \ h^{-1})^{3}$ including baryons and allowing for cooling and star formation. We find that, in models with dynamical dark energy, the evolving cosmological background leads to different star formation rates and different formation histories of galaxy clusters, but the baryon physics is not affected in a relevant way. We investigate several proxies for the cluster mass function based on X-ray observables like temperature, luminosity, $M_{gas}$, and $Y_{X}$. We confirm that the overall baryon fraction is almost independent of the dark energy models within few percentage points. The same is true for the gas fraction. This evidence reinforces the use of galaxy clusters as cosmological probe of the matter and energy content of the Universe. We also study the $c-M$ relation in the different cosmological scenarios, using both dark matter only and hydrodynamical simulations. We find that the normalization of the $c-M$ relation is directly linked to $\sigma_{8}$ and the evolution of the density perturbations for $\Lambda$CDM, RP and SUGRA, while for EQp and EQn it depends also on the evolution of the linear density contrast. These differences in the $c-M$ relation provide another way to use galaxy clusters to constrain the underlying cosmology.