Discrete Symmetries in Translation Invariant Cosmological Models

In this paper we investigate a class of (d + 1) dimensional cosmological models with a cosmological constant possessing an R^d simply transitive symmetry group and show that it can be written in a form that manifests the effect of a permutation symmetry. We investigate the solution orbifold and calculate the probability of a certain number of dimensions that will expand or contract. We use this to calculate the probabilities up to dimension d = 5.