Dynamics of the mixmaster-type vacuum universe with geometry R×S3×S3×S3
Abstract
A model of a spatially homogeneous and anisotropic, vacuum universe with geometry R×S ×S ×S is studied using a hamiltonian formalism. The formalism is developed by first deriving the hamiltonian for a D-dimensional, mixmaster-type, vacuum universe. The model evolves from an initial Kasner-like state to a final Kasner-like state upon irreversible collapse. The collapse is predicted to be inevitable based on qualitative analysis and numerical calculations verify this behavior. A lower bound of 0.286 is found for the ratio of the contraction rate of the universe long after a Kasner phase transition to the contraction rate long before the transition. Seven of the seventeen theoretically possible qualitatively different compactification schemes are found numerically and tabulated. A subset of all the constraint satisfying initial conditions which leads to three isotropically expanding dimensions and six contracting dimensions is found. © 1990 Plenum Publishing Corporation. 3 3 3
