Thermal/quantum effects and induced superstring cosmologies

We consider classical superstring theories on flat four-dimensional space-times, and where N=4 or N=2 supersymmetry is spontaneously broken. We obtain the thermal and quantum corrections at the string one-loop level and show that the back-reaction on the space-time metric induces a cosmological evolution. We concentrate on heterotic string models obtained by compactification on a T6 torus and on T6/Z2 orbifolds. The temperature T and the supersymmetry breaking scale M are generated via the Scherk-Schwarz mechanism on the Euclidean time cycle and on an internal spatial cycle respectively. The effective field theory corresponds to a no-scale supergravity, where the corresponding no-scale modulus controls the SUSY-breaking scale. The classical flatness of this modulus is lifted by an effective thermal potential, given by the free energy. The gravitational field equations admit solutions where M, T and the inverse scale factor 1/a of the universe remain proportional. In particular the ratio M/T is fixed during time evolution. The induced cosmology is governed by a Friedmann-Hubble equation involving an effective radiation term ∼1/a4 and an effective curvature term ∼1/a2, whose coefficients are functions of the complex structure ratio M/T.