The XMM-LSS survey:: the Class 1 cluster sample over the initial 5 deg2 and its cosmological modelling

We present a sample of 29 galaxy clusters from the XMM-LSS survey over an area of some 5 deg(2) 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, obtained from dedicated spatial and spectral fitting. 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-X-T(z) relation points towards 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-X-T relation, which may explain the contradictory results from previous studies. Extensive simulations show that extending the survey area to 10 deg(2) has the potential to exclude the non-evolution hypothesis, but those constraints on more refined intracluster medium models will probably be limited by the large intrinsic dispersion of the L-X-T relation, whatever be the sample size. We further demonstrate that increasing the dispersion in the scaling laws increases the number of detectable clusters, hence generating further degeneracy [in addition to sigma(8), Omega(m), L-X-T(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 Sunyaev-Zel'dovich surveys.