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The observed evolution of the galaxy cluster X-ray integral temperature distribution function between z=0.05 and z=0.32 is used in an attempt to constrain the value of the density parameter, Ω0, for both open and spatially flat universes. We estimate the overall uncertainty in the determination of both the observed and predicted galaxy cluster X-ray integral temperature distribution functions at z=0.32 by carrying out Monte Carlo simulations, where we take into careful consideration all the most important sources of possible error. We include the effect of the formation epoch on the relation between virial mass and X-ray temperature, improving on the assumption that clusters form at the observed redshift which leads to an overestimate of Ω0. We conclude that at present both the observational data and the theoretical modelling carry sufficiently large associated uncertainties to prevent an unambiguous determination of Ω0. We find that values of Ω0 around 0.75 are most favoured, with Ω0<0.3 excluded with at least 90 per cent confidence. In particular, the Ω0=1 hypothesis is found to be still viable as far as this data set is concerned. As a by-product, we also use the revised data on the abundance of galaxy clusters at z=0.05 to update the constraint on σ8 given by Viana & Liddle, finding slightly lower values than before.
Viana et al. (Mon,) studied this question.