Inflation and initial conditions in the pre-big-bang scenario

The pre-big-bang scenario describes the evolution of the Universe from an initial state approaching the flat, cold, empty, string perturbative vacuum. The choice of such an initial state is suggested by the present state of our Universe if we accept that the cosmological evolution is (at least partially) duality symmetric. Recently, the initial conditions of the pre-big-bang scenario have been criticized as they introduce large dimensionless parameters allowing the Universe to be “exponentially large from the very beginning.” We agree that a set of initial parameters (such as the initial homogeneity scale, the initial entropy) larger than those determined by the initial horizon scale $H^{-1}$ would be somewhat unnatural to start with. However, in the pre-big-bang scenario, the initial parameters are all bounded by the size of the initial horizon. The basic question thus becomes: is a maximal homogeneity scale of order $H^{-1}$ necessarily unnatural if the initial curvature is small and, consequently, $H^{-1}$ is very large in Planck (or string) units? In the impossibility of experimental information one could exclude a priori, for large horizons, the maximal homogeneity scale $H^{-1}$ as a natural initial condition. In the pre-big-bang scenario, however, pre-Planckian initial conditions are not necessarily washed out by inflation and are accessible (in principle) to observational tests, so that their naturalness could be also analyzed with a Bayesan approach, in terms of a posteriori probabilities.