The XMM-LSS survey: the Class 1 cluster sample over the initial 5 square degrees and its cosmological modelling

We present a sample of 29 galaxy clusters from the XMM-LSS survey over an area of some 5deg2 out to a redshift of z=1.05. The sample clusters, which represent about half of the X-ray clusters identified in the region, follow well defined X-ray selection criteria and are all spectroscopically confirmed. For all clusters, we provide X-ray luminosities and temperatures as well as masses. The cluster distribution peaks around z=0.3 and T =1.5 keV, half of the objects being groups with a temperature below 2 keV. Our L-T(z) relation points toward self-similar evolution, but does not exclude other physically plausible models. Assuming that cluster scaling laws follow self-similar evolution, our number density estimates up to z=1 are compatible with the predictions of the concordance cosmology and with the findings of previous ROSAT surveys. Our well monitored selection function allowed us to demonstrate that the inclusion of selection effects is essential for the correct determination of the evolution of the L-T relation, which may explain the contradictory results from previous studies. Extensive simulations show that extending the survey area to 10deg2 has the potential to exclude the non-evolution hypothesis, but that constraints on more refined ICM models will probably be limited by the large intrinsic dispersion of the L-T relation. We further demonstrate that increasing the dispersion in the scaling laws increases the number of detectable clusters, hence generating further degeneracy [in addition to sigma8, Omega_m, L(M,z) and T(M,z)] in the cosmological interpretation of the cluster number counts. We provide useful empirical formulae for the cluster mass-flux and mass-count-rate relations as well as a comparison between the XMM-LSS mass sensitivity and that of forthcoming SZ surveys.