The ROSAT Deep Cluster Survey: Constraints on Cosmology

We use the ROSAT Deep Cluster Survey (RDCS) to trace the evolution of the cluster abundance out to $z\simeq 0.8$ and constrain cosmological models. We resort to a phenomenological prescription to convert masses into $X$-ray fluxes and apply a maximum-likelihood approach to the RDCS redshift- and luminosity-distribution. We find that, even changing the shape and the evolution on the $L_{bol}$-$T_X$ relation within the observational uncertainties, a critical density Universe is always excluded at more than $3\sigma$ level. By assuming a non-evolving $X$-ray luminosity-temperature relation with shape $L_{bol}\propto T_X^3$, it is ${\mathrm{\Omega }}_m=0.35_{-0.25}^{+0.35}$ and ${\sigma }_8=0.76_{-0.14}^{+0.38}$ for flat models, with uncertainties corresponding to $3\sigma$ confidence levels.