Superstring cosmology for N₄ = 1 -> 0 superstring vacua

We study the cosmology of perturbative heterotic superstring theory during the radiation-like era for semi-realistic backgrounds with initial $\N=1$ supersymmetry. This analysis is valid for times after the Hagedorn era (or alternatively inflation era) but before the electroweak symmetry breaking transition. We find an attraction to a radiation-like era with the ratio of the supersymmetry breaking scale to temperature stabilized. This provides a dynamical mechanism for setting the supersymmetry breaking scale and its corresponding hierarchy with the Planck scale. For the internal space, we find that orbifold directions never decompactify, while toroidal directions may decompactify only when they are wrapped by certain geometrical fluxes which break supersymmetry. This suggests a mechanism for generating spatial directions during the radiation-like era. Moreover, we show that certain moduli may be stabilized during the radiation-like era with masses near the supersymmetry breaking scale. In addition, the moduli do not dominate at late times, thus avoiding the cosmological moduli problem.