Multidimensional cosmology and asymptotical AdS

TL;DR

This paper investigates a multidimensional gravitational model with quadratic curvature, showing that certain parameters lead to stabilized extra dimensions and an asymptotically AdS external space, linking higher-dimensional and 4D physics.

Contribution

It introduces a specific non-linear gravitational model with quadratic curvature, analyzing conditions for stabilization and asymptotic AdS behavior in a multidimensional setting.

Findings

Extra dimensions can be stabilized with negative curvature internal spaces.

The effective 4D cosmological constant is negative, leading to asymptotically AdS external space.

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

Abstract

A non-linear gravitational model with a multidimensional geometry and quadratic scalar curvature is considered. For certain parameter ranges, the extra dimensions are stabilized if the internal spaces have negative curvature. As a consequence, the 4-dimensional effective cosmological constant as well as the bulk cosmological constant become negative. The homogeneous and isotropic external space is asymptotically AdS. The connection between the D-dimensional and the 4-dimensional fundamental mass scales sets an additional restriction on the parameters of the considered non-linear models.