  We formulate the basic postulate of pre-big bang cosmology as one of
``asymptotic past triviality'', by which we mean that the initial state is a
generic perturbative solution of the tree-level low-energy effective action.
Such a past-trivial ``string vacuum'' is made of an arbitrary ensemble of
incoming gravitational and dilatonic waves, and is generically prone to
gravitational instability, leading to the possible formation of many black
holes hiding singular space-like hypersurfaces. Each such singular space-like
hypersurface of gravitational collapse becomes, in the string-frame metric, the
usual big-bang t=0 hypersurface, i.e. the place of birth of a baby Friedmann
universe after a period of dilaton-driven inflation. Specializing to the
spherically-symmetric case, we review and reinterpret previous work on the
subject, and propose a simple, scale-invariant criterion for collapse/inflation
in terms of asymptotic data at past null infinity. Those data should determine
whether, when, and where collapse/inflation occurs, and, when it does, fix its
characteristics, including anisotropies on the big bang hypersurface whose
imprint could have survived till now. Using Bayesian probability concepts, we
finally attempt to answer some fine-tuning objections recently moved to the
pre-big bang scenario.
