Can homogeneous extra dimensions be stabilized during matter domination?

Abstract

We investigate cosmologies with homogeneous extra dimensions that can be described by generalised Friedmann-Robertson-Walker metrics and give a brief review on a general setup to describe a broad range of standard stabilization and compactification mechanisms. These mechanisms allow for solutions to the field equations with static extra dimensions if the universe is dominated by radiation or an approximately constant energy-momentum tensor, as for example due to a cosmological constant. During matter domination, however, there are no static solutions for the extra dimensions and we therefore conclude that in this setup it is not possible to construct stabilization mechanisms for the whole evolution history of the universe. We furthermore show in detail that the two possible approaches of discussing either the higher-dimensional field equations directly or the dimensionally reduced and conformally transformed theory, are exactly equivalent and thus lead to the same conclusions. Finally, we indicate a possible way out of these difficulties.