The Cluster Temperature Function at High Redshift

We take advantage of the biggest cosmological simulation to date for a critical CDM universe in order to test robustness of the cluster mass function on a range of masses much wider than tested before. On the high mass end our results show an excess of hot clusters and a milder evolution compared to the analytical predictions based on the Press & Schechter formula. These features must be properly taken into account in deriving the cluster X-ray temperature function at moderate and high redshifts. On a general basis, the reduced negative evolution in the number of hot clusters could alleviate the discrepancies between the predictions for critical universes and incoming data, which instead seem to favour low Ω0.