Kaluza-Klein cosmology withN dilaton fields

Abstract

The ground state for Kaluza-Klein cosmological models with more than one dilaton field is considered. The dimensional reduction is performed and the equations of motion for the dilaton fields are considered. The normal modes of oscillation are found, one of them,ψ, being the conformai factor in front of the metric for the true four-dimensional space-time. It is shown that a stable minimum exists when both the cosmological term and all the scalar curvatures of the extra-dimensional subspaces are negative. If all these scalar curvatures are positive, the extra-dimensional subspaces collapse and the quantum effects should be taken into account to stabilize them. All other combinations of the signs of scalar curvatures lead to decompactification of some of the subspaces. Some cosmological applications are discussed. One of them concerns the possibility of constructing Big-Bang cosmological models starting from a nonsingular higher-dimensional space-time.