We use the ROSAT Deep Cluster Survey ( RDCS ) with the purpose of tracing 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 .
As a main result 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 \Omega _ { m } = 0.35 ^ { +0.35 } _ { -0.25 } and \sigma _ { 8 } = 0.76 ^ { +0.38 } _ { -0.14 } ( \Omega _ { m } = 0.42 ^ { +0.35 } _ { -0.27 } and \sigma _ { 8 } = 0.68 ^ { +0.21 } _ { -0.12 } ) for flat ( open ) models , while no significant constraints are found for the power–spectrum shape parameter \Gamma .
Uncertainties are 3 \sigma confidence levels for three significant fitting parameters .