Scalar fluctuations in dilatonic brane-worlds

We derive and solve the full set of scalar perturbation equations for a class of five-dimensional brane--world solutions, with a dilaton scalar field coupled to the bulk cosmological constant and to a 3-brane. The spectrum contains one localized massless scalar mode, to be interpreted as an effective dilaton on the brane, inducing long--range scalar interactions. Two massive scalar modes yield corrections to Newton's law at short distances, which persist even in the limit of vanishing dilaton (namely, in the standard Randall--Sundrum configuration).