Warped compactification on curved manifolds

TL;DR

This paper explores warped compactifications in supergravity, demonstrating that certain non-compact internal spaces and fluxes can produce four-dimensional de Sitter universes with finite Newton constants, challenging previous no-go theorems.

Contribution

It shows that warped compactifications with non-compact internal directions can yield 4D de Sitter solutions, extending beyond prior no-go results in classical supergravity.

Findings

Existence of classical solutions with non-compact internal spaces leading to de Sitter expansion.

Finite four-dimensional Newton constant and normalizable graviton zero-mode.

Fluxes can facilitate the realization of 4D de Sitter solutions in warped compactifications.

Abstract

The characterization of a six- (or seven)-dimensional internal manifold with metric as having positive, zero or negative curvature is expected to be an important aspect of warped compactifications in supergravity. In this context, Douglas and Kallosh recently pointed out that a compact internal space with negative curvature could help to construct four-dimensional de Sitter solutions only if the extra dimensions are strongly warped or there are large stringy corrections. That is, the problem of finding 4-dimensional de Sitter solutions is well posed, if all extra dimensions are physically compact, which is called a no-go theorem. Here, we show that the above conclusion does not extend to a general class of warped compactifications in classical supergravity that allow a non-compact direction or cosmological solutions for which the internal space is asymptotic to a cone over a product of compact Einstein spaces or spheres. For clarity, we present classical solutions that compactify higher-dimensional spacetime to produce a Robertson--Walker universe with de Sitter-type expansion plus one extra non-compact direction. Such models are found to admit both an effective four-dimensional Newton constant that remains finite and a normalizable zero-mode graviton wavefunction. We also exhibit the possibility of obtaining 4D de Sitter solutions by including the effect of fluxes (p-form field strengths).