Cosmological expansion on a dilatonic brane-world

We explore the nature of cosmological expansion induced by matter in a brane-world scenario with a bulk scalar field, such as a dliaton. We use a covariant formalism to obtain an expression for the effective 4D equations on the brane via projection, and hence deduce the expansion rate. We discuss in detail the effects of the bulk on the brane and how the scalar field can induce contributions to the expansion rate. These methods are applied to the Randall-Sundrum scenarios and to models suggested to stabilize the size of the extra-dimension using a scalar field, such as that due to Goldberger and Wise. We find that in such models the expansion rate is negative on a negative tension brane when the extra dimension is stabilized irrespective of whether there is a scalar field, contrary to some claims in the literature. The formalism can also be applied to cosmological applications of a Horava-Witten type model with and without a coupling between the scalar field and the matter on the brane. We compare and contrast these 'rolling-radius models' with 4D models in which fundamental constants vary. The coupling of the matter on thebrane to the scalar field appears to allow for the possibility of accelerated expansion on the brane driven by the effects of the bulk.