The duality-type symmetries of string cosmology naturally lead to a
pre-big-bang phase of accelerated evolution as dual counterpart of the
decelerated expansion of standard cosmology. We discuss several properties of
this scenario, including the possibility that tracks of the pre-big-bang may be
found either in the spectrum of relic gravitons or in the distortion they
induce on the cosmic microwave background.Comment: 36 pages (plus 1 table and 3 figures ava. upon request), CERN-TH.657