Inflationary Cosmologies from Compactification?

TL;DR

This paper analyzes compactifications of higher-dimensional gravity theories to lower-dimensional cosmologies, showing that most configurations do not produce inflation, except for some negatively curved cases with eternal but diminishing acceleration.

Contribution

It demonstrates that compactifications on Einstein spaces generally do not yield inflationary expansion in the resulting FLRW cosmology, clarifying limitations of such models.

Findings

No inflation in k=0,+1 cases due to scalar potential structure.

k=-1 case admits eternal acceleration with decreasing rate.

Compactifications do not produce large-scale inflationary expansion.

Abstract

We consider the compactification of (d+n)-dimensional pure gravity and of superstring/M-theory on an n-dimensional internal space to a d-dimensional FLRW cosmology, with spatial curvature k=-1,0,+1, in Einstein conformal frame. The internal space is taken to be a product of Einstein spaces, each of which is allowed to have arbitrary curvature and a time-dependent volume. By investigating the effective d-dimensional scalar potential, which is a sum of exponentials, it is shown that such compactifications, in the k=0,+1 cases, do not lead to large amounts of accelerating expansion of the scale factor of the resulting FLRW universe, and, in particular, not to inflation. The case k=-1 admits solutions with eternal accelerating expansion for which the acceleration, however, tends to zero at late times.