Measuring Ωmwith theROSATDeep Cluster Survey

We analyze the ROSAT Deep Cluster Survey (RDCS) to derive cosmological constraints from the evolution of the cluster X-ray luminosity distribution. The sample contains 103 galaxy clusters out to z similar or equal to 0.85 and flux limit F-lim = 3 x 10(-14) ergs s(-1) cm(-2) (RDCS-3) in the 0.5E2.0 keV energy band, with a high-redshift extension containing four clusters at 0.90 less than or equal to z less than or equal to 1.26 and brighter than F-lim = 1 x 10(-14) ergs s(-1) cm(-2) (RDCS-1). We assume cosmological models to be speciDed by the matter density parameter Omega (m), the rms fluctuation amplitude at the 8 h(-1) Mpc scale sigma (8), and the shape parameter for the cold dark matter-like power spectrum Gamma. Model predictions for the cluster mass function are converted into the X-ray luminosity function in two steps. First, we convert mass into intracluster gas temperature by assuming hydrostatic equilibrium. Then, temperature is converted into X-ray luminosity by using the most recent data on the L-X-T-X relation for nearby and distant clusters. These include the Chandra data for six distant clusters at 0.57 less than or equal to z less than or equal to 1.27. From RDCS-3 we find Omega (m) = 0.35(-0.10)(+0.13) and sigma (8) = 0.66(-0.05)(+0.06) for a spatially flat universe with a cosmological constant, with no significant constraint on Gamma (errors correspond to 1 sigma confidence levels for three fitting parameters). Even accounting for both theoretical and observational uncertainties in the mass-X-ray luminosity conversion, an Einstein-de Sitter model is always excluded at far more than the 3 sigma level. We also show that the number of X-ray-bright clusters in RDCS-1 at z >0.9 is expected from the evolution inferred at z <0.9 data.