I report recent studies on the evolution of perturbations in the context of
the ``pre-big-bang" scenario typical of string cosmology, with emphasis on the
formation of a stochastic background of relic photons and gravitons, and its
possible direct/indirect observable consequences. I also discuss the possible
generation of a thermal microwave background by using, as example, a simple
gravi-axio-dilaton model whose classical evolution connects smoothly
inflationary expansion to decelerated contraction. By including the quantum
back-reaction of the produced radiation the model eventually approaches the
standard radiation-dominated (constant dilaton) regime.Comment: 37 pages, Plain TEX, 3 figures available by fax upon request, to
appear in Proc. of the Erice School on "String gravity and physics at the
Planck scale" (Erice, 8-19 September 1995
