The duality-type symmetries of string cosmology naturally lead us to expect a pre-big-bang phase of accelerated evolution as the dual counterpart of the decelerating expansion era of standard cosmology. Several properties of this scenario are discussed, including the possibility that it avoids the initial singularity and that it provides a large amount of inflation. We also discuss how possible tracks of the pre-big-bang era may be looked for directly in the spectral and "squeezing" properties of relic gravitons and, indirectly, in the distorsion they induce on the cosmic microwave background.

We review physical motivations, phenomenological consequences, and open problems of the so-called pre-big bang scenario in superstring cosmology. (C) 2002 Elsevier Science B.V. All rights reserved

We consider a late-time cosmological model based on a recent proposal that the infinite-bare-coupling limit of superstring or M theory exists and has good phenomenological properties, including a vanishing cosmological constant, and a massless, decoupled dilaton. As it runs away to ϩϱ, the dilaton can play the role of the quintessence field recently advocated to drive the late-time accelerated expansion of the Universe. If, as suggested by some string theory examples, appreciable deviations from general relativity persist even today in the dark matter sector, the Universe may smoothly evolve from an initial ''focusing'' stage, lasting until radiation-matter equality, to a ''dragging'' regime, which eventually gives rise to an accelerated expansion with frozen ⍀(dark energy)/⍀(dark matter).