We use the semi-analytic models of galaxy formation developed by Kauffmann, White & Guiderdoni to generate predictions for the observed properties of cluster and group galaxies at redshifts between 0 and 0.6. We examine four sets of cosmological initial conditions: low-density CDM models with and without cosmological constant, a flat CDM model and a mixed dark matter model. These models were selected because they span a wide range in cluster formation epoch. The semi-analytic models that we employ are able to follow both the evolution of the dark matter component of clusters and the formation and evolution of the stellar populations of the cluster galaxies. We are thus able to generate model predictions that can be compared directly with the observational data. In the low-density CDM models, clusters form at high red- shift and accrete very little mass at recent times. Our models predict that essentially no evolution in the observed properties of clusters will have occurred by a redshift of 0.6, in direct contradiction with the data. In contrast, in the MDM model, both galaxies and clusters form extremely late. This model predicts evolution which appears to be too extreme to be in agreement with the observations. The flat CDM model, which is intermediate in structure formation epoch, is most successful. This model is able to account for the evolution of the blue fraction of rich clusters with redshift, the relationship between blue fraction and cluster richness at different epochs, and the changes in the distribution of the morphologies of cluster galaxies by a redshift of 0.4.
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