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SPATIALLY HOMOGENEOUS DYNAMICS : A UNIFIED PICTURE 1

The Einstein equations for a perfect fluid spatially homogeneous spacetime are studied in a unified manner by retaining the generality of certain parameters whose discrete values correspond to the various Bianchi types of spatial homogeneity. A parameter dependent decomposition of the metric variables adapted to the symmetry breaking effects of the nonabelian Bianchi types on the “free dynamics” leads to a reduction of the equations of motion for those variables to a 2-dimensional time dependent Hamiltonian system containing various time dependent potentials which are explicitly described and diagrammed. These potentials are extremely useful in deducing the gross features of the evolution of the metric vari-