On initial conditions and global existence for accelerating cosmologies from string theory

It is expected that the inflation paradigmwould be explained within superstring/Mtheory. The theory predicts that spacetime dimension is greater than four. Since observable spacetime dimension is four, it is thought that the extra dimensions would be compactified within Planck scale. Recently, it has been pointed out that it is possible to find cosmological solutions which exhibit a transient phase of accelerated expansion of the universe (like inflation) if the size of the compactified internal hyperbolic space depends on time and/or if they are S(pacelike)-brane solutions [EG, TP, WMNR]. In these models, exponential potential terms like V0e aψ appear, where ψ denotes the compactification volume or effective dilaton field, a is a coupling constant and V0 is positive number. Explicitly, a typical action for the case is of the form