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 S/N 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 S-Z 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 $\sim$10 and become comparable with those
from XXL clusters. Combining the two probes allows us to put constraints on
$\Omega_m$=0.316$\pm$0.060, $\sigma_8$=0.814$\pm$0.054, and $w$=-1.02$\pm$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.
