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

Download
Author
Jackson, John Philip
Date
1972Advisor
Woehler, Kai E.
Metadata
Show full item recordAbstract
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.
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.Collections
Related items
Showing items related by title, author, creator and subject.
-
Morphology of unstable waves in a baroclinic jet.
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 ... -
Barotropic Vortex Stability to Perturbations from Axisymmetry
Carr, L.E. III; Williams, R.T. (1989-10);Tropical cyclones and dynamically similar model vortices robustly maintain a near-axisymmetric horizontal structure where the vortex flow is strongly nonlinear in spite of persistent asymmetric forcing represented by ...