Measuring Ω0 from the entropy evolution of clusters

In this paper we have extended the entropy-driven model of cluster evolution developed by Bower in order to be able to predict the evolution of galaxy clusters for a range of cosmological scenarios. We have applied this model to recent measurements of the evolution of the L-x - T normalization and X-ray luminosity function in order to place constraints on cosmological parameters. We find that these measurements alone do not select a particular cosmological framework. An additional constraint is required on the effective slope of the power spectrum to break the degeneracy that exists between this and the background cosmology. We therefore include a theoretical calculation of the Omega(0) dependence on the power spectrum, based on the fold dark matter paradigm, which infers Omega(0) < 0.55 (0.1 < Omega(0) < 0.7 for Omega(0) + Lambda(0) = 1), at the 95 per cent confidence level. Alternatively an independent measurement of the slope of the power spectrum from galaxy clustering requires Omega(0) < 0.6 (Omega(0) < 0.65 for Omega(0) + Lambda(0) = 1 again to 95 per cent confidence; The rate of entropy evolution is insensitive to the values of Omega(0) considered, although it is sensitive to changes in the distribution of the intracluster medium.