Bianchi type I cosmological models

Citation

Jacobs, Kenneth Charles (1969) Bianchi type I cosmological models. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/KSSQ-R708. https://resolver.caltech.edu/CaltechETD:etd-10162002-080822

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. This thesis begins with a brief review of observations of cosmological interest and with a sketch of the "standard" spatially homogeneous and isotropic cosmological models of our Universe that are currently in vogue. Following this introduction we investigate in great detail anisotropic cosmologies and cosmological models of Bianchi Type I. Our primary goal is to understand the consequences of expansion anisotropies in the general relativistic, hot big-bang theory of cosmology. We use the Einstein field equations with vanishing cosmological constant, and Maxwell's equations, to study the temporal evolution of anisotropic Bianchi Type I cosmologies. These cosmologies are spatially homogeneous, but anisotropic; and they have no rotation. We consider only cosmologies with the "flat", diagonal, Bianchi Type I metric ds[superscript 2] - dt[superscript2] - A[superscript 2](t)dx[superscript 2] - B[superscript 2](t)dy[superscript 2] - C[superscript 2](t)dz[superscript 2]. We begin by studying the general properties of Bianchi Type I cosmologies. Then we consider the stress-energy tensor for massless-particle gases (either degenerate or non-degenerate) which decouple from thermal equilibrium and become freely-propagating in our diagonal Bianchi Type I metric. We investigate the dynamical effects of anisotropic neutrino stresses, and we show how neutrino viscosity damps out most of the existing expansion anisotropies when neutrinos decouple. Finally, we elucidate the structure and properties of the Einstein field equations for anisotropic Bianchi Type I cosmologies by deriving a large number of analytical and numerical solutions to these equations. Our stress-energy tensor consists, in general, of perfect-fluid matter with the barotropic equation of state p[subscript m] = [gamma] [rho][subscript m] (0 [<=] [gamma] [<=] 1), and a uniform comoving magnetic field, with energy-density [rho][subscript b], aligned along the z-axis. We first consider the PERFECT-FLUID case where [rho][subscript b] = 0. We find the general analytical solution (for all [gamma]), and construct semi-realistic cosmological models of our Universe using this solution. Then we consider the PERFECT-FLUID-MAGNETIC case where [rho][subscript b] [is not equal to] 0. We derive several analytical solutions, find the behavior near the initial physical singularity for the remaining cases, and study those remaining cases by numerical integration of the field equations. We then consider semi-realistic PERFECT-FLUID-MAGNETIC cosmological models of our Universe. In our semi-realistic cosmological models we study the possible effects of expansion anisotropies and of a uniform primordial magnetic field upon the following: (a) the type of initial physical singularity, (b) the thermal history and temporal evolution of our Universe, (c) primordial element formation, (d) the time when expansion anisotropies become small, and (e) the temperature isotropy of the observed 2.7[degrees]K cosmic microwave radiation.

Thesis Files