Kaluza-Klein Inflation with Non-Minimally Coupled Scalar Field

Abstract

Introduction The idea of the Kaluza-Klein theory has been regarded as one of the most interesting approaches for a unification of all fundamental interactions including gravity.I) A crucial point for the theory to be realistic is to explain why the space is so small that one cannot observe it and why the ordinary space is so large. An interesting attempt to this problem is what is called cosmological dimensional reduction, according to which the large discrepancy of two sizes is regarded as a consequence of the dynamical evolution of the higher-dimensional universe.) Furthermore, the external space experiences an inflationary expansion phase during the contraction of the internal space, and it is hoped to solve the well-known horizon and the flatness problems. ) So far, most of such models assume that the space-time has a direct-product. topology like R x S3 X sn from the beginning and that the universe is filled with a perfect-fluid-type matter or merely vacuum. . Above all, the direct-product ansatz plays a critical role in the dynamical compactification, but it seems there has been no reasonable explanation for the splitting of two subspaces. Another great concern is whether the. kind of matter and its coupling to gravity has some influence or not upon the dynamical behavior of the universe, in particular on its inflationary evolution. In the case of usual 4-dimensional space-times, it has been pointed out that a non-minimal coupling between a scalar field and gravity prevents the inflationary scenario to work for some range of 1;.4) Therefore, we may naively expect such a co¥pling to have a significant effect on the behavior of the higherdimensional universe, too.