The Most Distant X-ray Clusters and the Evolution of their Space Density
  We briefly review our current knowledge of the space density of distant X-ray clusters as measured by several ROSAT serendipitous surveys. We compare old and new determinations of the cluster X-ray Luminosity Function (XLF) at increasing redshifts, addressing the controversial issue of the evolution of its high end. We use complete subsamples, drawn from the ROSAT Deep Cluster Survey (RDCS), to quantify the statistical significance of the XLF evolution out to z ~1. A consistent observational picture emerges in which the bulk of the cluster population shows no significant evolution out to z ~1, whereas the most luminous systems (L_x >~ L* [0.5-2 keV] =~ 5x10^44 erg/s) were indeed rarer, at least at z >0.5, in keeping with the original findings of the EMSS. We also report on the recent spectroscopic identification of four clusters in the RDCS lying beyond z =1, the most distant X-ray clusters known to date, which set an interesting lower limit on the space density of clusters at z >1. 
P. Rosati (1), S. Borgani (2), R. Della Ceca (3), S.A. Stanford (4),   P.R. Eisenhardt (5), C. Lidman (1) ((1) ESO, (2) INFN...