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, T crit ∼ m 3 / 2 M P ( 3 / β ) 3 / 4 K ′ ′ − 1 / 4 . For realistic models we find T crit ∼ 10 11 – 10 12 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