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 \simeq 0.85 and flux–limit F _ { lim } = 3 \times 10 ^ { -14 } { erg s ^ { -1 } cm ^ { -2 } } ( RDCS-3 ) in the [ 0.5–2.0 ] keV energy band , with a high–redshift extension containing four clusters at 0.90 \leq z \leq 1.26 and brighter than F _ { lim } = 1 \times 10 ^ { -14 } { erg s ^ { -1 } cm ^ { -2 } } ( RDCS-1 ) .
We assume cosmological models to be specified by the matter density parameter \Omega _ { m } , the r.m.s .
fluctuation amplitude at the 8 h ^ { -1 } { Mpc } scale \sigma _ { 8 } , and the shape parameter for the CDM–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 intra–cluster 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 seven distant clusters at 0.57 \leq z \leq 1.27 .
From RDCS-3 we find \Omega _ { m } = 0.35 ^ { +0.13 } _ { -0.10 } and \sigma _ { 8 } = 0.66 ^ { +0.06 } _ { -0.05 } for a spatially flat Universe with 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 are expected from the evolution inferred at z < 0.9 data . Subject headings : Cosmology : theory - dark matter - galaxies : clusters : general - X-rays : galaxies