  Classical and quantum gravitational instabilities, can, respectively, inflate
and warm up a primordial Universe satisfying a superstring-motivated principle
of "Asymptotic Past Triviality". A physically viable big bang is thus generated
without invoking either large fine-tunings or a long period of post-big bang
inflation. Properties of the pre-bangian Universe can be probed through its
observable relics, which include: i) a (possibly observable) stochastic
gravitational-wave background; ii) a (possible) new mechanism for seeding the
galactic magnetic fields; iii) a (possible) new source of large-scale structure
and CMB anisotropy.
