String windings in the early universe

TL;DR

This paper investigates string dynamics in the early universe, modeling it as a 9-torus with excited strings, and finds that while three large dimensions can emerge, this is statistically unlikely.

Contribution

It provides an analytical and numerical study of string winding modes in a homogeneous anisotropic universe, assessing their role in dimension decompactification.

Findings

Three large spatial dimensions can emerge dynamically.

Such an outcome is statistically disfavored under the model's assumptions.

The evolution depends on initial conditions and string interactions.

Abstract

We study string dynamics in the early universe. Our motivation is the proposal of Brandenberger and Vafa, that string winding modes may play a key role in decompactifying three spatial dimensions. We model the universe as a homogeneous but anisotropic 9-torus filled with a gas of excited strings. We adopt initial conditions which fix the dilaton and the volume of the torus, but otherwise assume all states are equally likely. We study the evolution of the system both analytically and numerically to determine the late-time behavior. We find that, although dynamical evolution can indeed lead to three large spatial dimensions, such an outcome is not statistically favored.