The Isotropy of Compact Universes
Abstract
We discuss the problem of the stability of the isotropy of the universe in the space of ever-expanding spatially homogeneous universes with a compact spatial topology. The anisotropic modes which prevent isotropy being asymptotically stable in Bianchi-type VIIh universes with non-compact topologies are excluded by topological compactness. Bianchi type V and type VIIh universes with compact topologies must be exactly isotropic. In the flat case we calculate the dynamical degrees of freedom of Bianchi-type I and VII0 universes with compact 3-spaces and show that type VII0 solutions are more general than type I solutions for systems with perfect fluid, although the type I models are more general than type VII0 in the vacuum case. For particular topologies the 4-velocity of any perfect fluid is required to be non-tilted. Various consequences for the problems of the isotropy, homogeneity, and flatness of the universe are discussed.
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