The fine tuning problem in pre-big-bang inflation

We examine the effect of spatial curvature in the pre-big-bang inflationary model suggested by string theory. We study $O(\alpha ')$ corrections and we show that, independently of the initial curvature, they lead to a phase of exponential inflation. The amount of inflation in this phase is long enough to solve the horizon and flatness problems if either the evolution starts deeply into the weak coupling regime or the analogous of a slow roll condition is satisfied.