Dynamics of the mixmaster-type vacuum universe with geometry \(R\times S^ 3\times S^ 3\times S^ 3\) (Q753171)

The authors study a model of a spatially homogeneous and anisotropic, vacuum universe with geometry \(R\times S^ 3\times S^ 3\times S^ 3\) using a hamiltonian formalism. The motivation for this study is the exploration of the geometrical dynamics of the early universe where anisotropic spatial curvature terms dominate over matter and radiation terms in the field equations. It is found that this universe evolves from an initial Kasner-like state bound for irreversible and inevitable collapse. Once the universe has collapsed, it develops into one of seventeen physically unique final Kasner-like states. Seven of the seventeen theoretically possible qualitatively different compactification schemes are found numerically and tabulated. The results about the collapse are based on qualitative analysis and numerical calculations.