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
Joaquim Anacleto and Joaquim Alberto C Anacleto 2008 Eur. J. Phys. 29 555
Shaaban Khalil 2002 J. Phys. G: Nucl. Part. Phys. 28 2207
Chao Li et al 2008 J. Phys. D: Appl. Phys. 41 032005
W B Bonnor 2001 Class. Quantum Grav. 18 233
Björn Sandstede and Arnd Scheel 2000 Nonlinearity 13 1465
S Ochiai et al 2003 Supercond. Sci. Technol. 16 1071
Sutirtha Mukhopadhyay et al 2009 New J. Phys. 11 055002
S A Merkulov 1992 Class. Quantum Grav. 9 2267
M Hasenbusch and K Pinn 1997 J. Phys. A: Math. Gen. 30 63