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.

6 pages, no figures, latex2e using ltwol2e.sty. Based on talks at the 44'th annual meeting of the Israel Physical Society, Apr 8, 1998, Rehovot, Israel, and ICHEP98, 23-29 July, Vancouver, BC, Canada, and second conf. on Quantum Aspects of Gauge Theories, Supersymmetry and Unification, Sept 21-26, 1998, Corfu, Greece. To be published in the proceedings