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Abstract  The well defined selection function of the XMM‐LSS surveys enables a simultaneous modelling of the observed cluster number counts and of the evolution of the  L  X ‐ T  X  relation. We present results pertaining to the first 5 deg 2  for a well controlled sample comprising 30 objects: they are compatible with the WMAP3 parameter set along with cluster selfsimilar evolution. Extending such a survey to 200 deg 2  would (1) allow discriminating between the major scenarios of the cluster  L  X ‐ T  X  evolution and (2) provide a unique self‐sufficient determination of σ 8  and Γ with an accuracy of ∼5% and 10% respectively, when adding mass information from weak lensing and S‐Z observations. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The XMM‐LSS cluster sample and its cosmological applications: Prospects for the XMM next decade