The analogue potential of Kaluza-Klein cosmology with Euler form actions

Abstract

Abstract The cosmological implications of a D -dimensional Kaluza-Klein theory based on Euler form actions are investigated. The D -dimensional manifold is taken to be a direct product of a Robertson-Walker space-time and an irreducible homogeneous internal space. For an equation of state with zero internal pressure, the time evolution of space-time is shown to be governed by an analogue potential. The world radius starts evolving either from zero or from a finite initial value and the expansion can be Friedmann-like or inflationary, depending on the type of solution. For solutions where the world radius starts evolving from a nonzero value, transitions between the two types of expansion are allowed. A simple statistical model indicates that the inflationary potential dominates at the early stages of the evolution of the universe whereas the Friedmann-like potential dominates at the later stages.