The behaviour of point masses in an expanding cosmological substratum.

We investigate the properties of point masses imbedded in a smooth, expanding cosmological substratum, which has an equation of state similar to that of radiation. We formulate a model in which the dynamics of the whole ensemble of point masses is taken into account, and study its evolution beginning from small perturbations through a stability analysis. The results imply that there cannot be at present hidden mass in the form of neutrinos or gravitational waves, of density significantly exceeding that of galaxies, since then clusters of galaxies would not have been able to form. We also apply the results to models of the early universe in which the presence of primeval black holes is hypothesized, and conclude that over scales less than the horizon, fluctuations in the black hole number density cannot grow as long as the equation of state of the universe is of the radiation type.