Density perturbations in a cosmological de Donder gauge

Density perturbations are considered during the radiation-dominated and the dust-dominated periods of the expanding universe. The perturbations are taken to have spherical symmetry and the investigation is carried out in the de Donder gauge. In order to guarantee the energy-momentum conservation of the perturbation in the de Donder gauge a compatibility condition is obtained. Equations for the propagation of a spherically symmetric perturbation in linear approximation on a FRW cosmological background are presented. It turns out that the evolutiontendency of the formation is mainly predicted by the state of the cosmic background. A radiation-dominated universe does not stimulate growth processes; the perturbation will be in a frozen state or it will diffuse. It is found that the dust-dominated universe stimulates the perturbation mass to grow. The rate of this cosmic affected growing process is proportional toR^–1 (R being the scale factor of the universe), so that it seems that almost all galaxies were formed at the beginning of the present dust-dominated era.