  We discuss bounds on the dilaton mass, following from the cosmological
amplification of the quantum fluctuations of the dilaton background, under the
assumption that such fluctuations are dominant with respect to the classical
background oscillations. We show that if the fluctuation spectrum grows with
the frequency the bounds are relaxed with respect to the more conventional case
of a flat or decreasing spectrum. As a consequence, the allowed range of masses
may become compatible with models of supersymmetry breaking, and with a
universe presently dominated by a relic background of dilaton dark matter.
