Regularised field equations for Bianchi type VI spatially homogeneous cosmology

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Abstract
Using Jantzen's Lie algebra automorphism formalism and the scale invariance of the Einstein equations, it is shown that there is a natural way of compactifying the gravitational phase space for spatially homogeneous cosmology, thereby allowing standard qualitative geometric techniques from the theory of ordinary differential systems to be used to find the asymptotic behaviour of solutions near the initial singularity and in the distant future. In this way the field equations for Bianchi type VIh (including III=VI-1) cosmologies are reduced to a seven-dimensional first-order system on a physical phase space with compact closure. It turns out that the natural time parameter for this system coincides with Misner's Omega -time. Furthermore, the system is analytic in the interior of the phase space, a feature which seems to be limited to Bianchi types III, IV and VI. The extent to which the system can be extended to the boundary is discussed. Some critical points of the reduced system give rise to a new class of exact solutions which includes rotating models. Finally, the system is specialised to a Taub-like four-dimensional subsystem in which some explicit calculations are done.

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