Cosmological models with weakly turbulent fluctuations of the metric superimposed on a homogeneous and isotropic background metric

Abstract

Uniform and isotropic mathematical models of the expanding universe usually predict an initial singularity of infinite mass density and space curvature. To study possible mechanisms which would avoid the occurance of these singularities, non-uniform cosmological models based on Einstein's field equations are investigated in which random perturbations of long wave lengths are superimposed on the Robinson- Walker metric of the unperturbed models. Techniques of fluid turbulence theory, used to describe random fields by a hierarchy of central moments of the random perturbations, are applied to describe the dynamics of these moments. For the case of small perturbations the hierarchy is truncated and solutions are found. The solutions are either growing or decaying perturbations leading to Rᴹ extra terms in the usual cosmological equations for the curvature radius R. The result agrees with the small perturbation Fourier series expansion analysis which exists in the literature. Based on the upper limit of the anisotropy of the 3° K background radiation, the growing perturbation model predicts a maximum expansion even for k=0, Euclidean spaces. The decaying perturbation solutions give extra terms of the form 1/Rᴹ with m>4 in the cosmological equations and indicate that the mechanism of long wave random perturbations may prevent the original singularity and make oscillatory models possible.