Dynamics of the mixmaster-type vacuum universe with geometryR×S 3×S 3×S 3 |
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Authors: | W. M. Stuckey L. Witten Bob Stewart |
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Affiliation: | (1) Physics Department, Elizabethtown College, 17022 Elizabethtown, Pennsylvania, USA;(2) Department of Physics, University of Cincinnati, 45221 Cincinnati, Ohio, USA;(3) Optistract, Inc., 45213 Cincinnati, Ohio, USA |
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Abstract: | A model of a spatially homogeneous and anisotropic, vacuum universe with geometryR×S3×S3×S3 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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