Accelerating Cosmologies from Compactification

TL;DR

A solution of the (4+n)-dimensional vacuum Einstein equations is found for which spacetime is compactified on an n-dimensional compact hyperbolic manifold to a flat four-dimensional Friedmann-Lemaitre-Robertson-Walker cosmology undergoing a period of accelerated expansion in the Einstein conformal frame.

Abstract

A solution of the (4+n)-dimensional vacuum Einstein equations is found for which spacetime is compactified on a compact hyperbolic manifold of time-varying volume to a flat four-dimensional FLRW cosmology undergoing accelerated expansion in Einstein conformal frame. This shows that the `no-go' theorem forbidding acceleration in `standard' (time-independent) compactifications of string/M-theory does not apply to `cosmological' (time-dependent) hyperbolic compactifications.

Figures (2)

• Figure 1: The function $m(t)$ for $n=7$ is compared to the sqare root of the right hand side of relation (\ref{['acc']}), in small dashes. The difference is plotted in wide dashes and is positive in the interval of acceleration.
• Figure 2: The scale factor $S(\eta)$ of the four-dimensional universe is shown for $n=7$ and $\kappa=1$. It clearly exhibits an accelerating phase.