Hyperbolic Space Cosmologies

TL;DR

This paper explores accelerating cosmologies derived from M/string theory compactifications on hyperbolic spaces, revealing conditions for eternal acceleration and exact solutions, including Milne and intersecting S-brane configurations.

Contribution

It systematically analyzes hyperbolic space compactifications in M/string theory, providing new exact solutions and conditions for eternal acceleration in four-dimensional cosmologies.

Findings

Hyperbolic compactifications can produce accelerating universes.

Eternal acceleration occurs for internal spaces with dimension ≥7.

Positive definite potentials with local minima support eternal acceleration.

Abstract

We present a systematic study of accelerating cosmologies obtained from M/string theory compactifications of hyperbolic spaces with time-varying volume. A set of vacuum solutions where the internal space is a product of hyperbolic manifolds is found to give qualitatively the same accelerating four-dimensional FLRW universe behavior as a single hyperbolic space. We also examine the possibility that our universe is a hyperbolic space and provide exact Milne type solutions, as well as intersecting S-brane solutions. When both the usual 4D spacetime and the m-dimensional internal space are hyperbolic, we find eternally accelerating cosmologies for $m\geq 7$, with and without form field backgrounds. In particular, the effective potential for a magnetic field background in the large 3 dimensions is positive definite with a local minimum and thus enhances the eternally accelerating expansion.