Gauge couplings at high temperature and the relic gravitino abundance

In higher-dimensional supersymmetric theories gauge couplings of the effective four-dimensional theory are determined by expectation values of scalar fields. We find that at temperatures above a critical temperature T-*, which depends on the supersymmetry breaking mass scales, gauge couplings decrease like T-alpha, alpha > 1. This has important cosmological consequences. In particular it leads to a relic gravitino density which becomes independent of the reheating temperature for T-R > T-*. For small gravitino masses, m(3/2) much less than m((g) over bar), the mass density of stable gravitinos is essentially determined by the gluino mass. The observed value of cold dark matter, Ohm(CDM)h(2) similar to 0.1, is obtained for gluino masses m((g) over bar) = O(1 TeV). (C) 2003 Published by Elsevier B.V.