Compactification of extra dimensions in quantum inhomogeneous Kaluza-Klein cosmological models

Quantum dynamics of inhomogeneous Kaluza-Klein cosmological models in the vicinity of a cosmological singularity is considered. It is shown that in the early universe if the number of dimensions D is less than or equal to ten, mean values of the metric indicate the existence of the initial stage of a compactification process. It is shown that such a behaviour of the mean values does not depend on a particular choice of an initial quantum state and, therefore, is a general property of the quantum evolution in the inhomogeneous Kaluza-Klein cosmologies.