  The production of a background of super-horizon curvature perturbations with
the appropriate (red) spectrum needed to trigger the cosmic anisotropies
observed on large scales is associated, in the context of pre-big bang
inflation, with a phase of growing string coupling. The extension towards the
past of such a phase is not limited in time by the dynamical backreaction of
the quantum perturbations of the cosmological geometry and of its sources. A
viable, slightly red spectrum of scalar perturbations can thus be the output of
an asymptotic, perturbative regime which is well compatible with an initial
string-vacuum state satisfying the postulate of "Asymptotic Past Triviality".
