Dilaton Destabilization at High Temperature

Many compactifications of higher–dimensional supersymmetric theories have approximate vacuum degeneracy. The associated moduli fields are stabilized by non–perturbative effects which break supersymmetry. We show that at finite temperature the effective potential of the dilaton acquires a negative linear term. This destabilizes all moduli fields at sufficiently high temperature. We compute the corresponding critical temperature which is determined by the scale of supersymmetry breaking, the β–function associated with gaugino condensation and the curvature of the Kähler potential, Tcrit ∼ √ m3/2MP (3/β) 3/4 K ′′−1/4. For realistic models we find Tcrit ∼ 1011–1012 GeV, which provides an upper bound on the temperature of the early universe. In contrast to other cosmological constraints, this upper bound cannot be circumvented by late–time entropy production.