Metric perturbations in dilaton-driven inflation

We compute the spectrum of scalar and tensor metric perturbations generated, as amplified vacuum fluctuations, during an epoch of dilaton-driven inflation of the type occurring naturally in string cosmology. In the tensor case the computation is straightforward while, in the scalar case, it is made delicate by the appearance of a growing mode in the familiar longitudinal gauge. In spite of this, a reliable perturbative calculation of perturbations far outside the horizon can be performed by resorting either to appropriate gauge invariant variables, or to a new coordinate system in which the growing mode can be ``gauged down". The simple outcome of this complicated analysis is that both scalar and tensor perturbations exhibit nearly Planckian spectra, whose common ``temperature" is related to some very basic parameters of the string-cosmology background.