It is known that the symptotic states of a large class of spatially homogeneous cosmological models, near the big bang and at late times, are described by exact self-similar solutions. With this as motivation the authors find all spatially homogeneous solutions of the Einstein field equations which have an orthogonal perfect fluid as source, or are vacuum, and admit a similarity group H 4 which acts transitively on spacetime.
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Hsu et al. (1986) studied this question.
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