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/a ⁴ and a curvature term ∼ 1/a², whose coefficients are functions of ratio of the gravitino mass scale to the temperature.