A lower limit of the cosmic mean density from the ages of clusters of galaxies

The presence of substructure in clusters of galaxies indicates that they have recently formed or accreted a significant fraction of their mass. The cosmic time at which this occurs is set in large part by the density of that region of space at very large redshift. If the distribution of density perturbations at high redshift is Gaussian, then the frequency of subclustering now is set by the mean density at recombination. Thus, the observed frequency of subclustering can be used to constrain. Surprisingly, plausible values of Lambda have little effect on this result. Unless three independent evaluations of the incidence of subclustering are all overestimates, or substructure lasts significantly longer than a crossing time in clusters, or perturbations at high redshift are not Gaussian, the universe is fairly dense (Omega sub 0 greater than about 0.5). The same line of argument suggests that direct observations (e.g., with Rosat) of evolution of the cluster population with shifts will provide a complementary direct measure of Omega sub 0.