Cosmological Solutions in String Theories

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We obtain a large class of cosmological solutions in the toroidally-compactified low energy limits of string theories in D dimensions. We consider solutions where a p-dimensional subset of the spatial coordinates, parameterising a flat space, a sphere, or an hyperboloid, describes the spatial sections of the physically-observed universe. The equations of motion reduce to Liouville or SL(N+1,R) Toda equations, which are exactly solvable. We study some of the cases in detail, and find that under suitable conditions they can describe four-dimensional expanding universes. We discuss also how the solutions in D dimensions behave upon oxidation back to the D=10 string theory or D=11 M-theory.