On the Initial Conditions for Pre-Big-Bang Cosmology

The beautiful scenario of pre-big-bang cosmology is appealling not only because it is more or less derived from string theory, but also because it separates clearly the problem of the initial conditions for the universe from that of high curvatures. Recently, the pre-big-bang program was subject to attack from on the grounds that pre-big-bang cosmology does not solve the horizon and flatness problems in a ``natural'' way, as customary exponential ``new'' inflation does. In particular, it appears that an arbitrarily small deviation from perfect flatness in the initial state can not be accommodated. For this analysis, matter in the universe before the big bang was assumed to be radiation. We perform a similar analysis to theirs, but using the equation of state for ``string matter'' $\rho=-3p$ which seems more appropriate to the physical situation and, also, is motivated by the scale factor duality (in the flat case) with respect to our expanding, radiation dominated, universe. For an open universe we find, exactly, the same time-dependence of the scale factor as in the Milne universe, recently found to represent the universal attractor at $t=-\infty $ of all pre big bang cosmologies. We conclude that our radiation dominated universe comes from a flat rather than a curved region.