Consistency of the Kaluza-Klein ansatz for cosmological solutions

A consistency problem for the Kaluza-Klein ansatz is shown to arise when the kinetic term of extra gauge fields depends on the internal coordinates. Consequences on cosmological solutions are discussed. A position-dependent kinetic term implies either a very special condition to be satisfied by it, or the time-independent size of internal space and the maximally symmetric universe in the vacuum. (orig.)