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.