Cosmological expansion on a dilatonic brane-world

In this paper we study brane-world scenarios with a bulk scalar field, using a covariant formalism to obtain a four-dimensional Einstein equation via projection onto the brane. We discuss, in detail, the effects of the bulk on the brane and how the scalar field contributes to the gravitational effects. We also discuss the choice of conformal frame and show that the frame selected by the induced metric provides a natural choice. We demonstrate our formalism by applying it to cosmological scenarios of Randall-Sundrum- and Horava-Witten-type models. Finally, we consider the cosmology of models where the scalar field couples non-minimally to the matter on the brane. This gives rise to a novel scenario where the universe expands from a finite scale factor with an initial period of accelerated expansion, thus avoiding the singularity and flatness problem of the standard big-bang model.