Dynamics of the mixmaster-type vacuum universe with geometryR×S 3×S 3×S 3

Details Dynamics of the mixmaster-type vacuum universe with geometryR×S 3×S 3×S 3 Dynamics of the mixmaster-type vacuum universe with geometryR×S 3×S 3×S 3

Nov 1990

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990gregr..22.1321s&link_type=abstract

General Relativity and Gravitation, Volume 22, Issue 11, pp.1321-1339

Computer Science

1

Scientific paper

A model of a spatially homogeneous and anisotropic, vacuum universe with geometryR×S 3×S 3×S 3 is studied using a hamiltonian formalism. The formalism is developed by first deriving the hamiltonian for aD-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.

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