John D Barrow and Hideo Kodama 2001 Class. Quantum Grav. 18 1753 doi:10.1088/0264-9381/18/9/310
John D Barrow1 and Hideo Kodama2
Show affiliationsWe 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 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 a 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.
Issue 9 (7 May 2001)
Received 2 January 2001
John D Barrow and Hideo Kodama 2001 Class. Quantum Grav. 18 1753
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