Probing dark energy with the next generation X-ray surveys of galaxy clusters
We present forecasts on the capability of future wide-area high-sensitivity X-ray surveys of galaxy clusters to yield constraints on the parameters defining the Dark Energy (DE) equation of state (EoS). Our analysis is carried out for future X-ray surveys which have enough sensitivity to provide accurate measurements of X-ray mass proxies and Fe-line based redshifts for about 2x10^4 clusters. We base our analysis on the Fisher Matrix formalism, by combining information on the cluster number counts and power spectrum, also including, for the first time in the analysis of the large scale cluster distribution, the effect of linear redshift-space distortions (RSDs). This study is performed with the main purpose of dissecting the cosmological information provided by geometrical and growth tests, which are both included in the analysis of number counts and clustering of galaxy clusters. We compare cosmological constraints obtained by assuming different levels of prior knowledge of the parameters which define the observable-mass X-ray relation. This comparison further demonstrates the fundamental importance of having a well calibrated observable-mass relation and, most importantly, its redshift evolution. Such a calibration can be achieved only by having at least $\sim 10^3$ net photon counts for each cluster included in the survey. We show that RSDs in the power spectrum analysis carry important cosmological information also when traced with galaxy clusters and the DE FoM increases by a factor of 8. Besides confirming the potential that large cluster surveys have in constraining the nature of DE, our analysis emphasizes that a full exploitation of the cosmological information carried by such surveys requires not only a large statistic but also a robust measurement of the mass proxies and redshifts for a significant fraction of the cluster sample, derived from the same X-ray survey data.