Hyperbolic space cosmologies

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 ≥ 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.

Towards Kaluza-Klein Dark Matter on nilmanifolds

“…In order to have a physical spectrum, we now reintroduce the dimensional parameters mentioned in section 2.1, namely r m , f, and we also want to include c. We obtain 17) while the orthonormal modes are given by …”

Inflation from superstring and M-theory compactification with higher order corrections

“…Since we are interested in cosmological solutions, we take the metric of our D-dimensional space as 11) with 12) where D = 1 + p + q. The external p-and internal q-dimensional spaces (ds 2 p and ds 2 q ) are chosen to be maximally symmetric.…”

Accelerating Universes from Compactification on a Warped Conifold

“…The past few years have witnessed significant progress in building of inflation models within string theory via flux compactifications of the ten-or eleven-dimensional spacetime of superstring or M theory with the desire to find models for late-time cosmology [3][4][5] supporting a small positive cosmological constant. If one wishes to stay within the realm of low energy supergravity models derived from superstrings, cosmic inflation is ruled out for warped flux compactifications of classical supergravities on the basis of a ''no-go'' theorem [6,7], which forbids accelerating solutions for warped (and static) extra dimensions.…”

“…It has the potential to offer a resolution to the dilemma posed by the observed cosmic acceleration within a natural theoretical framework. In [4] (and generalizations thereof [5]) the no-go theorem was circumvented just by the choice of negatively curved internal spaces, once the fluxes are turned off. The restriction on the curvature seems a severe one, especially given the view that flat space compactifications on Calabi-Yau spaces are among the most natural in string theory.…”

“…It has been learned that the timevarying volume moduli with no initial fine tuning among the scalars lead only to a transient period of cosmic acceleration, except in the case that we live in a hyperbolic Universe [5]. To fully account for the nature of an effective four-dimensional cosmology, it is important to gain a proper description of spacetime dependent compactifications (of higher dimensional gravity), rather than the time-dependent or the space-dependent (warped) compactification alone.…”