Simplicial Lattice Methods in Cosmology
Abstract
Since the publication by Friedmann of the solutions of Einstein's equations which were to found the study of Cosmology, it has undergone a process of continual refinement. Work has concentrated on improvements to the standard model of Cosmology, with the Friedmann solutions as a starting point. More sophisticated models for the matter were included, and less restrictive geometries were explored. Recently, several authors have begun to investigate the quantum behavior of these models. This thesis brings to bear numerical methods and the simplicial lattices of Regge on the problem. We first investigate the cosmology of the Einstein action. We find an initial suppression of isotropy in the quantum regime, which damps out completely in the classical regime. In the classical regime, all configurations are found to be equally weighted before inclusion of the prefactor. Once the prefactor is included, a weak favoring of anisotropy is found at small volumes, which damps out as a small peak about isotropy develops. The classical trajectories evolve towards isotropy, and suppress perturbations. The second project explores the application of the Regge Calculus to curvaturesquared actions. A general proposal of Hamber and Williams is considered in two dimensions. Additional precision is needed to understand the continuum limit, and this resolves the question into two separate cases, representing two different methods for taking the continuum limit. In one case it is found that none of the HW actions are found to behave correctly in the continuum limit. In the other case a unique member of the HW family is proved to have the correct continuum behavior.
 Publication:

Ph.D. Thesis
 Pub Date:
 1989
 Bibcode:
 1989PhDT.........4E
 Keywords:

 REGGE CALCULUS;
 Physics: Astronomy and Astrophysics;
 Astronomical Models;
 Continuums;
 Cosmology;
 Lattices (Mathematics);
 Mathematical Models;
 Quantum Theory;
 Regge Poles;
 Anisotropy;
 Isotropy;
 Particle Trajectories;
 Perturbation;
 Astrophysics