ON KALUZA–KLEIN COSMOLOGY

A generalization of Friedmann–Robertson–Walker cosmology to 4 + K dimensions is considered. The space-time manifold R¹ × S³ × S^K is characterized by two time-dependent scales, R (t) and a (t). The equations of motion for R and a are derived from the 4 + K-dimensional Einstein action supplemented by a one-loop thermal term, corresponding to a gas of non-interacting scalar particles. It is shown that in the approximation when T < 1/a the equations of motion admit a solution in which the internal space has a constant radius a while the external R(t) evolves in the usual manner.