Thermodynamical Stability of Hagedorn and Radiation Regimes in Closed String Gas Cosmology

TL;DR

This paper explores the thermal equilibrium conditions in closed string gas cosmology, focusing on Hagedorn and radiation regimes, revealing how string length and system size influence energy requirements for equilibrium.

Contribution

It analyzes thermal equilibrium in different regimes of closed string gas cosmology, highlighting the effects of string length and system size on energy and pressure relations.

Findings

Short strings in small Hagedorn regime require high energy for equilibrium.

Long strings in small Hagedorn regime achieve equilibrium with less energy.

Thermal equilibrium exists in all cases within the radiation regime.

Abstract

In this paper, we investigate thermal equilibrium in string gas cosmology which is dominated by closed string.We consider two interesting regimes, Hagedorn and radiation regimes.We find that for short strings in small radius of Hagedorn regime very large amount of energy requested to have thermal equilibrium but for long strings in such system a few energy is sufficient to have thermal equilibrium. On the other hand in the large radius of Hagedorn regime, which pressure is not negligible, we obtain a relation between the energy and pressure in terms of cosmic time which is satisfied by thermal equilibrium. Then we discuss about radiation regime and find that in all cases there is thermal equilibrium.