(ed.). Gravitational waves (IOP, 2001)(422s).

294 Elementary introduction to pre-big bang cosmologystandardevolutionapre-big banginflationaãSHRINKING HORIZONFigure 16.5. Qualitative evolution of the Hubble horizon (broken curve) and of the scalefactor (full curve) in the pre-big bang inflationary scenario, in the S-frame, a(t), and in theE-frame, ã(t).the initial portion of the universe may be very large in strings (or Planck) units,but not larger than the initial horizon itself [23], as emphasized in the picture.The initial horizon is large because the initial curvature scale is small, in stringunits, H i ≪ 1/λ s .This is a basic consequence of the choice of the initial state which, in thepre-big bang scenario, approaches the flat, cold and empty string perturbativevacuum [8], and which is to be contrasted to the extremely curved, hot anddense initial state of the standard scenario, characterizing a universe which startsinflating at the Planck scale, H i ∼ 1/λ p .16.4 Open problems and phenomenological consequencesIn order to give an honest presentation of the pre-big bang scenario, it is fairto say that the string cosmology models are not free from various (more or lessimportant) difficulties, and that many aspects of the scenario are still unclear. Adetailed discussion of such aspects is outside the purpose of this paper, but wewould like to mention here at least three important open problems. Presentedin ‘time-ordered’ form (from the beginning to the end of inflation) they are thefollowing.• The first concerns the initial conditions, and in particular the decay of thestring perturbative vacuum. The question is whether or not the ‘switching on’