The rate of growth of density perturbations in simple big-bang model universes

In this paper we present exact solutions to the density perturbation equation derived by Bonnor for the cases where = _c ,k=1 and = – _c ,k=–1. The solutions when =0,k=1 and =0,k=–1 have been previously published. Using these solutions a quantitative analysis has been carried out that has enabled us to estimate the size of the fluctuations that must be postulated at decoupling in order to explain the formation of the galaxies in these model universes.