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

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