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 which grow 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 worldsheets 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.
Greene, B., Kabat, D., & Marnerides, S. (2010). Dynamical decompactification and three large dimensions. Physical Review D - Particles, Fields, Gravitation and Cosmology, 82(4) DOI: 10.1103/PhysRevD.82.043528