On three dimensions as the preferred dimensionality of space via the Brandenberger-Vafa mechanism

TL;DR

This paper explores how successive thermal fluctuations in string cosmology favor three spatial dimensions becoming large, supporting the Brandenberger-Vafa mechanism's prediction of a three-dimensional universe.

Contribution

It extends previous work by analyzing the impact of multiple fluctuations and string coupling strength on the emergence of three large spatial dimensions.

Findings

Successive fluctuations can lead to a three-dimensional large universe.

Large string coupling increases the likelihood of three dimensions expanding.

Further detailed studies are needed to confirm the assumptions.

Abstract

In previous work it was shown that, in accord with the Brandenberger-Vafa mechanism, three is the maximum number of spatial dimensions that can grow large cosmologically from an initial thermal fluctuation. Here we complement that work by considering the possibility of successive fluctuations. Suppose an initial fluctuation causes at least one dimension to grow, and suppose successive fluctuations occur on timescales of order alpha'^{1/2}. If the string coupling is sufficiently large, we show that such fluctuations are likely to push a three-dimensional subspace to large volume where winding modes annihilate. In this setting three is the preferred number of large dimensions. Although encouraging, a more careful study of the dynamics and statistics of fluctuations is needed to assess the likelihood of our assumptions.