The growth of density perturbations in zero pressure Friedmann-Lemaitre universes

Abstract

The amplification of density perturbations existing at the epoch of decoupling and which become bound within the linear regime of gravitational-instability theory and subsequently collapse into protogalaxies is calculated in the context of zero-pressure Friedmann-Lemaitre universes. The various cosmological models obtained as solutions to the Friedmann differential equation are classified in terms of the deceleration and density parameters. Analytical solutions to the density-perturbation equation for zero, positive, and negative cosmological constants are presented in terms of redshift, density parameter, and deceleration parameter. Conditions are derived for bound perturbations, which will eventually collapse into discrete systems, and the amplification of density perturbations existing at the epoch of decoupling is evaluated numerically for two different values each of the density parameter and the decoupling redshift. The results show that amplification increases with decreasing values of the deceleration parameter.