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. 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 2 x 10(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. 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 relation between cluster mass and X-ray observables. This comparison further demonstrates the fundamental importance of having a well calibrated observablemass relation and, most importantly, its redshift evolution. Such a calibration can be achieved only by having at least similar to 103 net photon counts for each cluster included in the survey, with sufficient angular resolution. We show that redshift-space distortions in the power spectrum analysis carry important cosmological information also when traced with galaxy clusters. We find that the DE figure of merit increases by a factor of 8 when including the effect of such distortions. 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 redshift for a significant fraction of the cluster sample, which ought to be derived from the same X-ray survey data. This will be possible with future X-ray surveys, such as those envisioned with the Wide Field X-ray Telescope, with an adequate combination of survey area, sensitivity and angular resolution.