Lovelock type brane cosmology

Abstract

The cosmological implications of the geodetic brane gravity model, enhanced by geometrical terms of Gibbons-Hawking-York (GHY) type and Gibbons-Hawking-York-Myers type (GHYM), carefully constructed as combinations of intrinsic and extrinsic curvatures, are examined. All the geometrical terms under study belong to a set named Lovelock-type brane models. The combined model gives rise to a second-order differential equation of motion. Under a Friedmann-Robertson-Walker (FRW) geometry defined on a $(3+1)$-dimensional world volume, together with a perfect fluid matter content, the emerging universe of this model evolves in a 5-dimensional Minkowski background, yielding peculiar facts. The resulting Friedmann-type equation is written in terms of energy density parameters, where fine-tuning is needed to probe interesting cosmological processes close to the current data. In this sense, Lovelock-type brane models might underlie the cosmic acceleration. Indeed, we find that these correction terms become significant at low energies/late times. The model exhibits self-accelerating (non-self-accelerating) behavior for the brane expansion, and in the case where the radiation-like contribution due to the existence of the extra dimension vanishes its behavior is the same as the Dvali-Gabadadze-Porrati (DGP) brane cosmology and its generalization to the Gauss-Bonnet (GB) brane gravity. Likewise, Einstein cosmology is recovered when the radiation-like contribution fades away along with the odd polynomials in brane extrinsic curvature.