Asymptotical AdS from non-linear gravitational models with stabilized extra dimensions

TL;DR

This paper explores non-linear gravitational models with extra dimensions, demonstrating that under certain conditions, the external universe becomes asymptotically Anti-de Sitter due to stabilized negative curvature extra dimensions.

Contribution

It shows that quadratic scalar curvature models can stabilize extra dimensions with negative curvature, leading to an asymptotically AdS 4D universe, and establishes parameter restrictions linking fundamental scales.

Findings

Extra dimensions are stabilized with negative constant curvature.

The effective 4D cosmological constant becomes negative, resulting in an asymptotically AdS space.

Parameter restrictions relate the D-dimensional and 4-dimensional fundamental mass scales.

Abstract

We consider non-linear gravitational models with a multidimensional warped product geometry. Particular attention is payed to models with quadratic scalar curvature terms. It is shown that for certain parameter ranges, the extra dimensions are stabilized if the internal spaces have negative constant curvature. In this case, the 4-dimensional effective cosmological constant as well as the bulk cosmological constant become negative. As a consequence, the homogeneous and isotropic external space is asymptotically AdS. The connection between the D-dimensional and the 4-dimensional fundamental mass scales sets a restriction on the parameters of the considered non-linear models.