The XXL Survey XXV. Cosmological analysis of the C1 cluster number counts

Context. We present an estimation of cosmological parameters with clusters of galaxies. Aims. We constrain the Omega m, sigma(8), and w parameters from a stand-alone sample of X-ray clusters detected in the 50 deg(2) XMM-XXL survey with a well-defined selection function. Methods. We analyse the redshift distribution of a sample comprising 178 high signal-to-noise ratio clusters out to a redshift of unity. The cluster sample scaling relations are determined in a self-consistent manner. Results. In a lambda cold dark matter (Lambda CDM) model, the cosmology favoured by the XXL clusters compares well with results derived from the Planck Sunyaev-Zel'dovich clusters for a totally different sample (mass/redshift range, selection biases, and scaling relations). However, with this preliminary sample and current mass calibration uncertainty, we find no inconsistency with the Planck CMB cosmology. If we relax the w parameter, the Planck CMB uncertainties increase by a factor of similar to 10 and become comparable with those from XXL clusters. Combining the two probes allows us to put constraints on Omega(m) = 0.316 +/- 0.060, sigma(g) = 0.814 +/- 0.054, and w = -1.02 +/- 0.20. Conclusions. This first self-consistent cosmological analysis of a sample of serendipitous XMM clusters already provides interesting insights into the constraining power of the XXL survey. Subsequent analysis will use a larger sample extending to lower confidence detections and include additional observable information, potentially improving posterior uncertainties by roughly a factor of 3.