Hyperbolic Space Cosmologies
Chiang-Mei Chen, Pei-Ming Ho, Ishwaree P. Neupane, Nobuyoshi Ohta, and, John E. Wang

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 , 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.
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