Dimensional reduction of the Kaluza-Klein universe due to the production of scalar particles

The semiclassical self-consistent model of a minimally coupled massless scalar field in a five-dimensional homogeneous universe is examined in order to study a possible cosmological mechanism of compactification in the Kaluza-Klein approach. The energy-momentum tensor of real particles is calculated under the assumption that the temperature is much less than the inverse of the diameter of the internal space. It is shown that there exists a family of solutions with the internal-space diameter approaching a constant and the Friedmann expansion law for the observable dimensions at late times. All of these solutions are characterized by zero initial temperatures. The initial values of the internal-space diameter, the curvature scalar, and the scale factors are free parameters.