  We consider the cosmological amplification of a metric perturbation
propagating in a higher-dimensional Brans-Dicke background, including a non
trivial dilaton evolution. We discuss the properties of the spectral energy
density of the produced gravitons (as well as of the associated squeezing
parameter), and we show that the present observational bounds on the graviton
spectrum provide significant information on the dynamical evolution of the
early universe.
