Nonlinear multidimensional gravity and cosmology

Abstract:
We consider cosmological models in multidimensional gravity with a Lagrangian containing a function of the Ricci scalar as well as the Ricci tensor squared and the Kretschmann invariant. Spatially flat isotropic cosmologies are built in a Kaluza-Klein approach with compact extra spaces of arbitrary dimension, with the aid of a slow-change approximation (as compared with the Planck scale). In particular, in some models with two extra factor spaces, we can obtain scenarios combining (i) primordial inflation with parameters compatible with the observational data and (ii) modern accelerated expansion, accompanied by a slow decrease of the effective gravitational constant within observational limits. This class of models predicts a slow growth of the extra scale factors which should ultimately lead to drastic changes in the physical laws of our Universe.

This is joint work with S.G. Rubin.