Numerical Experiments in String Cosmology

TL;DR

This paper uses numerical experiments to explore string thermodynamics in a toroidal universe, revealing phase transitions and decay behaviors of winding modes that support a string cosmology scenario explaining space dimensionality.

Contribution

It provides new numerical evidence on the thermodynamics and phase transitions of string networks, especially regarding winding mode decay and implications for cosmology.

Findings

At low energy density, short closed loops dominate.

A phase transition occurs at the Hagedorn temperature with formation of long winding loops.

Long winding strings decay only in three spatial dimensions.

Abstract

We investigate some classical aspects of fundamental strings via numerical experiments. In particular, we study the thermodynamics of a string network within a toroidal universe, as a function of string energy density and space dimensionality. We find that when the energy density of the system is low, the dominant part of the string is in the form of closed loops of the shortest allowed size, which correspond to the momentum string modes. At a certain critical energy density corresponding to the Hagedorn temperature, the system undergoes a phase transition characterized by the formation of very long loops, winding a number of times around the torus. These loops correspond to the winding string modes. As the energy density is increased, all the extra energy goes into these long strings. We then study the lifetime of winding modes as a function of the space densionality. We find that in the low--energy density regime, long winding strings decay only if the space dimensionality of the toroidal universe is equal to 3. This finding supports the proposed cosmological scenario by Brandenberger and Vafa, which attempts to explain the space dimensionality and to avoid the initial singularity by means of string theory.