Inflationary solutions with a five dimensional complex scalar field

We discuss inflationary solutions of the coupled Einstein-Klein-Gordon equations for a complex field in a five dimensional spacetime with a compact $x^5$-dimension. As a new feature, the scalar field contains a dependence on the extra dimension of the form $\exp(i m x^5) $, corresponding to Kaluza-Klein excited modes. In a four dimensional picture, a nonzero $m$ implies the presence of a new term in the scalar field potential. An interesting feature of these solutions is the possible existence of several periods of oscillation of the scalar field around the equilibrium value at the minimum of the potential. These oscillations lead to cosmological periods of accelerated expansion of the universe.