Lecture notes on thermodynamics of ideal string gases and its application in cosmology

TL;DR

This paper provides a pedagogical overview of the thermodynamics of ideal string gases, focusing on the Hagedorn temperature, phase structure, and applications in cosmology, including early universe models and moduli stabilization.

Contribution

It offers a detailed, explicit computation framework for string gas thermodynamics and explores its implications for cosmological phenomena and stability mechanisms.

Findings

Analysis of the Hagedorn temperature and associated instabilities

Moduli-dependent phase structure and stabilization mechanisms

Application to radiation-dominated early universe models

Abstract

In these lecture notes I give a pedagogical introduction to the thermodynamics of ideal string gases. The computation of thermodynamic quantities in the canonical ensemble formalism will be shown in detail with explicit examples. Attention will be given mainly to the thermodynamical consequences of string degrees of freedom, where I will especially address i) the Hagedorn temperature, a critical temperature above which the canonical ensemble description breaks down, which can be the onset point of some instability of the string gas; ii) the phase structure arising from compactification, embodied in the moduli-dependence of the Helmholtz free energy, which corrects the tree-level vacuum and can provide mechanism for moduli stabilization. Then I will briefly explain the implementation of string gas thermodynamics in cosmology, showing a simple example which gives rise to a radiation-dominated early universe. Further phenomenological issues and open questions will be discussed qualitatively with references indicated, including the Hagedorn instability in the resolution of the initial singularity, moduli stabilization, generation of hierarchy, radiative symmetry breaking and primordial cosmological fluctuations.