GLOBAL PROPERTIES OF LOCALLY SPATIALLY HOMOGENEOUS COSMOLOGICAL MODELS WITH MATTER

The existence and nature of singularities in locally spatially homogen eous solutions of the Einstein equations coupled to various phenomenol ogical matter models is investigated. It is shown that, under certain reasonable assumptions on the matter, there are no singularities in an expanding phase of the evolution and that unless the spacetime is emp ty a contracting phase always ends in a singularity where at least one scalar invariant of the curvature diverges uniformly. The class of ma tter models treated includes perfect fluids, mixtures of non-interacti ng perfect fluids and collisionless matter.