Investigation of Density Perturbation Growth within Generalized Field Equations

Abstract

We extend a previous work where a nonlinear perturbation equation based on Generalized Field Equation was deduced assuming a flat universe. In this paper a more general nonlinear perturbation equation which can be utilized in both flat and non-flat universes was derived. It consists of nonlinear terms in density perturbation and its derivatives. The deduced fourth order nonlinear equation consists of terms that are supposed to be responsible of strong and weak gravitational fields. Thus the equation can be utilized to study density perturbations in the presence of either strong or weak fields. The equation was used to investigate the possibility of perturbation growth using different scales of expansion of the universe assuming the sole presence of matter energy density. The different scales of expansion were obtained from the solution of the contracted version of the Generalized Field Equation. Constant nonlinear density perturbations were obtained in a curved universe, while constant or decaying ones were obtained in a flat expanding universe, the obtained results were comparable with previous works.