Spatially-homogeneous Vlasov-Einstein dynamics
| Title: | Spatially-homogeneous Vlasov-Einstein dynamics |
| Author: | Okabe, Takahide |
| Abstract: | The influence of matter described by the Vlasov equation, on the evolution of anisotropy in the spatially-homogeneous universes, called the Bianchi cosmologies, is studied. Due to the spatial-homogeneity, the Einstein equations for each Bianchi Type are reduced to a set of coupled ordinary differential equations, which has Hamiltonian form with the metric components being the canonical coordinates. In the vacuum Bianchi cosmologies, it is known that a curvature potential, which comes from the symmetries of the three-dimensional Lie groups, determines the basic properties of the evolution of anisotropy. In this work, matter potentials are constructed for Vlasov matter. They are obtained by first introducing a new matter action principle for the Vlasov equation, in terms of a conjugate pair of functions, and then enforcing the symmetry to obtain a reduction. This yields an expression for the matter potential in terms of the phase space density, which is further reduced by assuming cold streaming matter. Some vacuum Bianchi cosmologies and Type I with Vlasov matter are compared. It is shown that the Vlasov-matter potential for cold streaming matter results in qualitatively distinct dynamics from the well-known vacuum Bianchi cosmologies. |
| Department: | Physics |
| Subject: |
General relativity (Physics)--Mathematics
Cosmology--Mathematical models Hamiltonian systems Lie algebras Lie groups Anisotropy |
| URI: | http://hdl.handle.net/2152/18198 |
| Date: | 2008-12 |
Files in this work
This work appears in the following Collection(s)
-
UT Electronic Theses and Dissertations
ETD is a collection of UT Austin authored electronic dissertations.