Peculiar velocities of galaxy clusters, and the mean density of matter in the universe

It is shown that observations of the peculiar velocities of galaxies and clusters might yield valuable information on deceleration and density parameters as well as on the spectrum of large-scale density irregularities in the universe with a characteristic size much greater than 100 Mpc. On such scales, any density irregularities are of low amplitude, and the linear theory for the evolution of perturbations in the density and velocity of matter applies. Within the framework of this theory, equations are derived to describe how perturbations in the velocity of matter will evolve as the universe expands. It is shown that the course of this evolution depends strongly on the mean density of matter in the universe.