Cosmological aspects of the heterotic string above the Hagedorn temperature

Abstract

We consider the cosmology of the heterotic string above the grand-unification scale taking into account the thermodynamical phase structure of an ideal gas of heterotic string excitations above the Hagedorn temperature. We find that the Universe expands up to a critical volume ${a}_{c}^{9}$ above which the massive (Planckian) excitations should decay into massless excitations (nonequilibrium regime). The Universe then goes on expanding in a radiation-dominated phase with a scale factor a(t)\ensuremath{\sim}\ensuremath{\beta}(t). Because the heterotic string is self-dual with respect to temperature, it is argued that there is an induced duality relation for the scale factor a(t).