Phase Space of Compact Bianchi Models with Fluid

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.