Dynamics of compact homogeneous universes

Abstract

A complete description of dynamics of compact locally homogeneous universes is given, which, in particular, includes explicit calculations of Teichmüller deformations and careful counting of dynamical degrees of freedom. We regard each of the universes as a simply connected four dimensional spacetime with identifications by the action of a discrete subgroup of the isometry group. We then reduce the identifications defined by the spacetime isometries to ones in a homogeneous section, and find a condition that such spatial identifications must satisfy. This is essential for explicit construction of compact homogenoeus universes. Some examples are demonstrated for Bianchi II, VI${}_0$, VII${}_0$, and I universal covers.

32 pages with 2 figures (LaTeX with epsf macro package)

References in corpus (2)

• Strong cosmic censorship in vacuum space--times with compact, locally homogeneous Cauchy surfaces
• Compact Homogeneous Universes

Cited by in corpus (15)

• The QCD nature of Dark Energy
• The Isotropy of Compact Universes
• Instantons and unitarity in quantum cosmology with fixed four-volume
• On Closed Einstein-de Sitter Universes
• Cosmological Einstein-Yang-Mills equations
• Dimensional reduction and gauge group reduction in Bianchi-Type cosmology
• The Calabi complex and Killing sheaf cohomology
• Hamiltonian structures for compact homogeneous universes
• Perturbations of Spatially Closed Bianchi III Spacetimes
• Locally U(1)*U(1) Symmetric Cosmological Models: Topology and Dynamics
• Thurston's Geometrization Conjecture and cosmological models
• New varieties of Gowdy spacetimes
• Harmonic Analysis of Linear Fields on the Nilgeometric Cosmological Model
• Scalar fields on SL(2,R) and H^2 x R geometric spacetimes and linear perturbations
• Bianchi cosmologies in a Thurston-based theory of gravity