RESULTS FROM THE ROSAT DEEP CLUSTER SURVEY

Deep X-ray surveys of galaxy clusters covering large solid angles offe r ideal samples for studying the evolution of the large scale structur e in the Universe. I review here some recent results from the ROSAT De ep Cluster Survey (RDCS), particularly, on the study of the evolution of the abundance of galaxy clusters over a large redshift range. The o ptical identification of RDCS sources have revealed a significant frac tion of clusters at z > 0.5. The observed X-ray Luminosity Function ou t to z similar or equal to 0.8 and the faint cluster number counts fro m the RDCS, when combined with previous results of the Einstein Extend ed Medium Sensitivity Survey, provide a much improved observational pi cture of the evolution of clusters in the X-ray band, revealing a slow ly evolving population of galaxy clusters since at least z similar or equal to 0.8. The theoretical interpretation of these findings in the framework of theories of structure formation will still be subject of much debate in the years to come. The construction of large samples of clusters out to z similar to 1 and beyond appears to be a challenging task even with the next generation of X-ray satellites (AXAF, XMM).