  Scale factor duality, a truncated form of time dependent T-duality, is a
symmetry of string effective action in cosmological backgrounds interchanging
small and large scale factors. The symmetry suggests a cosmological scenario
("pre-big-bang") in which two duality related branches, an inflationary branch
and a decelerated branch are smoothly joined into one non-singular cosmology.
The use of scale factor duality in the analysis of the higher derivative
corrections to the effective action, and consequences for the nature of exit
transition, between the inflationary and decelerated branches, are outlined. A
new duality symmetry is obeyed by the lowest order equations for inhomogeneity
perturbations which always exist on top of the homogeneous and isotropic
background. In some cases it corresponds to a time dependent version of
S-duality, interchanging weak and strong coupling and electric and magnetic
degrees of freedom, and in most cases it corresponds to a time dependent
mixture of both S-, and T-duality.
  The energy spectra obtained by using the new symmetry reproduce known results
of produced particle spectra, and can provide a useful lower bound on particle
production when our knowledge of the detailed dynamical history of the
background is approximate or incomplete.
