Phase Space of Compact Bianchi Models with Fluid

TL;DR

This paper analyzes the phase space structure of compact, locally homogeneous universe models with fluid, revealing how space topology influences the number of dynamical degrees of freedom, especially for complex topologies.

Contribution

It provides a detailed analysis of the phase space for compact Bianchi models with fluid, highlighting the impact of space topology on dynamical degrees of freedom, including previously incomplete results.

Findings

Space topology significantly affects dynamical degrees of freedom.

For certain models, degrees of freedom increase unboundedly with topology complexity.

Confirmed and extended previous results on Bianchi models with complex topologies.

Abstract

The structure of phase space is determined for spatially compact and locally homogeneous universe models with fluid. Analysis covers models with all possible space topologies except for those covered by S^3, H^3 or S^2xR which have no moduli freedom. We show that space topology significantly affects the number of dynamical degrees of freedom of the system. In particular, we give a detailed proof of the result that for the systems modeled on the Thurston types H^2xR and SL_2, which have locally the Bianchi type III or VIII symmetry, the number of dynamical degrees of freedom increases without bound when the space topology becomes more and more complicated, which was first pointed out by Koike, Tanimoto and Hosoya in an incomplete form.