Sensitive, wide-area X-ray surveys which would be possible with the WFXT will detect huge samples of virialized objects spanning the mass range from sub-groups to the most massive clusters, and extending in redshift to beyond z=2. These samples will
be an excellent dataset for carrying out many traditional cosmological tests using the cluster mass function and power spectrum. Uniquely, WFXT will be able not only to detect clusters but also to make detailed X-ray measurements for a large number of clusters and groups right from the survey data. Very high quality measurements of the cluster mass function and spatial correlation over a very wide range of masses, spatial scales, and redshifts, will be useful for expanding the cosmological discovery space, and in particular, in searching for departures from the concordant Lambda-CDM cosmological model. Finding such departures would have far-reaching implications on our understanding of the fundamental physics which governs the Universe.
We discuss the central role played by X-ray studies to reconstruct the past history of formation and evolution of supermassive Black Holes (BHs), and the role they played in shaping the properties of their host galaxies. We shortly review the progres
s in this field contributed by the current X-ray and multiwavelength surveys. Then, we focus on the outstanding scientific questions that have been opened by observations carried out in the last years and that represent the legacy of Chandra and XMM, as for X-ray observations, and the legacy of the SDSS, as for wide area surveys: 1) When and how did the first supermassive black holes form? 2) How does cosmic environment regulate nuclear activity (and star formation) across cosmic time? 3) What is the history of nuclear activity in a galaxy lifetime? We show that the most efficient observational strategy to address these questions is to carry out a large-area X-ray survey, reaching a sensitivity comparable to that of deep Chandra and XMM pointings, but extending over several thousands of square degrees. Such a survey can only be carried out with a Wide-Field X-ray Telescope (WFXT) with a high survey speed, due to the combination of large field of view and large effective area, i.e., grasp, and sharp PSF. We emphasize the important synergies that WFXT will have with a number of future groundbased and space telescopes, covering from the radio to the X-ray bands and discuss the immense legacy value that such a mission will have for extragalactic astronomy at large.
