Thermal duality and non-singular superstring cosmologies

We review the construction of superconformal field theories on the worldsheet, which describe superstring models where only a finite number of states are effectively thermalized. Compared to conventional superstring models at finite temperature, they are obtained by switching on suitable Wilson lines along the Euclidean time circle S1(R0). This discrete deformation forbids the appearance of tachyons at any radius R0 and restores a T-duality symmetry on the temporal cycle. This implies the existence of a maximal temperature Tc, which is equal to twice the standard Hagedorn temperature. The models obtained this way differ substantially from the usual thermal ones only in the regime where the temperature is of order of the string scale, when the canonical ensemble of the full superstring spectrum breaks down. In the tachyon free models, a transition occurs at the temperature Tc, which transforms a phase of pure Kaluza-Klein excitations along S1(R0) into a T-dual phase of pure winding modes. Thanks to the consistency of these thermal backgrounds, cosmological evolutions induced by the free energy are found in various dimensions, with neither Hagedorn instabilities nor initial singularities. They describe bouncing universes, which can be described consistently in perturbation theory throughout the evolution.