Dynamical Decompactification and Three Large Dimensions

TL;DR

This paper investigates string gas cosmology and demonstrates that interactions favor three large spatial dimensions, supporting the Brandenberger-Vafa mechanism, through suppression of interactions in higher dimensions and dynamics in the early universe.

Contribution

It provides a detailed analysis of string interactions and cosmological dynamics that supports the natural emergence of three large spatial dimensions.

Findings

Interaction rates are exponentially suppressed for d > 3 dimensions.

In the early universe, the universe remains in the Hagedorn regime unless fluctuations lead to a radiation regime.

Winding modes in d > 3 dimensions are diluted and freeze out, supporting the Brandenberger-Vafa mechanism.

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 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.