Thermal and quantum superstring cosmologies

We consider four dimensional heterotic string backgrounds for which supersymmetry is spontaneously broken via the Scherk‐Schwarz mechanism on an internal spatial cycle and by finite temperature effects. We concentrate on initially flat backgrounds with N = 4 and N = 2 amount of supersymmetry. Thermal and quantum corrections give rise to a non‐trivial cosmological evolution. We show that these corrections are under control and calculable due to the underlying no‐scale structure of the effective supergravity theory. The effective Friedmann‐Hubble equation involves a radiation term ∼1/a4 and a curvature term ∼1/a2 , whose coefficients are functions of ratio of the gravitino mass scale to the temperature.