Multidimensional cosmology and asymptotical AdS
  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. 
U. Guenther, P. Moniz, A. Zhuk