Pre-Big-Bang Requires the Universe to be Exponentially Large From the Very Beginning

We show that in a generic case of the pre-big-bang scenario, inflation will solve cosmological problems only if the universe at the onset of inflation is extremely large and homogeneous from the very beginning. The size of a homogeneous part of the universe at the beginning of the stage of pre-big-bang (PBB) inflation must be greater than $10^{19} l_s$, where $l_s$ is the stringy length. The total mass of inflationary domain must be greater than $10^{72} M_s$, where $M_s \sim l_s^{-1}$ is the stringy mass. If the universe is initially radiation dominated, then its total entropy at that time must be greater than $10^{68}$. If the universe is closed, then one can describe it in terms of effective action only at the ``stringy'' time $t_s \sim l_s$ after the initial singularity. At that moment initial distribution of matter must be uniform over $10^{24}$ causally disconnected domains. The natural duration of the PBB stage in this scenario is $M_p^{-1}$. If the universe is open, then its initial density should have been vanishingly small and very homogeneous over an infinitely large distance. We argue that this regime is unstable with respect to quantum fluctuations, which make the universe very inhomogeneous. A regime of eternal inflation does not occur in this scenario. This should be compared with the simplest versions of the chaotic inflation scenario, where the regime of eternal inflation may begin in a universe of a size $M_p^{-1}$ with vanishing initial entropy of radiation, and initial mass $O(M_p)$. We conclude that the current version of the PBB scenario cannot replace usual inflation even if one solves the graceful exit problem in this scenario.