The boost-like symmetry of Kaluza-Klein cosmologies

For a large class of toroidally compact, spacially flat Kaluza-Klein cosmological models, we display the existence of an additional dynamical symmetry. The corresponding conserved quantity F, is related to the anisotropy in the evolution of the Universe. In the context of the third quantized mini-superspace Wheeler-De Witt equation, for some of these models, we analyze the spontaneous creation of anisotropic universes from "nothing" with a resulting thermal distribution in the possible eigenvalues of F.