Why weakly non-linear effects are small in a zero-pressure cosmology

Abstract

According to the usual model, the early universe was initially smooth and isotropic. Structure is assumed to have emerged through the action of gravitational forces on a set of initial perturbations. Juszkiewicz (1981) has asserted that the nonlinear transfer of power to high frequencies from power at some large scale can have a dramatic effect on the perturbation spectrum. The present investigation has the objective to show that the result obtained by Juszkiewicz is due to an incomplete analysis. A calculation is presented of the first-order nonlinear interactions between density perturbations in an expanding, Newtonian cosmology.