Cosmological models with weakly turbulent fluctuations of the metric superimposed on a homogeneous and isotropic background metric
Jackson, John Philip
Woehler, Kai E.
MetadataShow full item record
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.
Approved for public release; distribution is unlimited.
Showing items related by title, author, creator and subject.
Lewis, Stanley P. (1964);Solution of a system of second-order partial differential equations obtained from linearized approximations to the vorticity and thermodynamic equations yields phase velocities and amplitude functions which are utilized ...
The numerical solution and analysis of airplane spin equations modeled in a fixed coordinate system Champoux, Robert Louis (1972-12);Three forms of the airplane spin equations of motion, derived by Buehler in Reference [l], form the basis for the development of a computer program designed to seek dynamically stable equilibrium solutions of a spinning ...
Carey, Edwin Fenton, Jr. (Naval Postgraduate School, Monterey, California, 1976-03);According to the linearized solutions for thermal blooming, the density perturbations become infinite (i.e. "catastrophic" defocusing) as the Mach number approaches unity. However, the nonlinearities in the transonic ...