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

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.