Initial Conditions in Pre-big Bang

This note is a summary of the work reported in hep-th/9801073. We give a brief discussion of the fine tuning problem in pre-big bang cosmology. We use the flatness problem as our test case, and in addition to the exact numerical limits on initial conditions, we highlight the differences between pre-big bang and standard inflation. The main difference is that in pre-big bang the universe must be smooth and flat in an exponentially large domain already at the beginning of the dilaton-driven inflation. It has been known at least for a decade that it is extremely hard to construct a working mechanism for inflation in string theory. The moduli fields, and in particular, the dilaton, tend to roll rapidly in the presence of vacuum energy, and this rolling slows down the cosmological expansion of the particle horizon. Hence the standard inflationary scenarios cannot work, since the horizon and flatness problems cannot be solved. One hopes that this problem is only temporary and that it will be eventually solved with the increasing understanding of string theory. But there is also a possibility that a different implementation of inflation might be possible. One of the most interesting suggestions in this direction has been the pre-big bang (PBB) scenario 1. This scenario attempts to use the rolling dilaton to run inflation. Due to this, there appear solutions which inflate superexponentially for some time in the string frame. In the course of this expansion, the curvature and the coupling would become large, and the evolution proceeds towards the curvature singularity (and not away from it). If one would assume the existence of a mechanism which could saturate the growth of the curvature and coupling, and overturn superexponential expansion into a subluminal power law one, one could match the solution onto a late time Friedmann-Robertson-Walker (FRW) one. The phase of strong curvature has been argued to resemble the Big Bang and the one preceding it has been dubbed the pre-big bang 1. Nevertheless, it has not been clear just how successful PBB is in explaining cosmological problems. In fact already in 1 it has been noted that at the onset of a Talk given at PASCOS-98 and at CAPP-98.