Dynamical decompactification and three large dimensions

Abstract

We study string gas dynamics in the early universe and seek to realize the Brandenberger-Vafa mechanism - a goal that has eluded earlier works - that singles out three or fewer spatial dimensions as the number that grows large cosmologically. Considering wound string interactions in an impact parameter picture, we show that a strong exponential suppression in the interaction rates for d>3 spatial dimensions reflects the classical argument that string world sheets generically intersect in at most four spacetime dimensions. This description is appropriate in the early universe if wound strings are heavy - wrapping long cycles - and diluted. We consider the dynamics of a string gas coupled to dilaton gravity and find that (a) for any number of dimensions the universe generically stays trapped in the Hagedorn regime and (b) if the universe fluctuates to a radiation regime any residual winding modes are diluted enough so that they freeze-out in d>3 large dimensions while they generically annihilate for d=3. In this sense the Brandenberger-Vafa mechanism is operative.