Kaluza-Klein gravity and scalar-tensor theories

In this paper, we propose a Kaluza-Klein approach to gravity in Delta=4+n(1)+n(2)+... dimensions, where n(1),n(2),... are the dimensions of independent internal spaces. One is interested in the case where each internal metric depends on the four-dimensional coordinates by a conformal factor. If all these conformal factors depend on the four-dimensional coordinates through a common scalar function Psi, the induced effective four-dimensional gravity theory turns out to be of general scalar-tensor type. One shows that, if there are at least two internal spaces, the theory is not ruled out by experimental tests on gravitation, even if there is no massive scalar-potential term in the effective four-dimensional Lagrangian (contrary to what happens if there is only one internal space, in which case omega is of order unity, whatever the dimension of this internal space).