The Isotropy of Compact Universes
release_wy7yld5o75gv7fouya6xic3pdq
by
John D. Barrow
2001
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 VII_h universes with non-compact
topologies are excluded by topological compactness. Bianchi type V and type
VII_h universes with compact topologies must be exactly isotropic. In the
flat case we calculate the dynamical degrees of freedom of Bianchi-type I and
VII_0 universes with compact 3-spaces and show that type VII_0 solutions
are more general than type I solutions for systems with perfect fluid,
although the type I models are more general than type VII_0 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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