Pregalaxy formation: A nonlinear analysis of the evolution of cosmological perturbations.

Abstract

A higher-order analysis of the evolution of cosmological perturbations in a Friedmann universe is given by using the PMF method. The essence of the PMF approach is to use a gauge where all fluctuations of the density, the pressure, and the four-velocity vanish. Additionally, a planar symmetry of the perturbations is assumed. In that gauge, even in higher orders, the perturbation field equations simplify considerably; they can be decoupled and, for simple equations of state, also be solved analytically. We give the solution for the dust universe up to third order. Comparison of these slutions strongly supports the conjecture that in general unstable perturbations grow much faster than they do according to the first-order analysis. However, perturbations with very large spatial extension behave differently; they grow only moderately. Thus, an upper boundary of the region of instability seems to exist.