Gauge couplings at high temperature and the relic gravitino abundance

Abstract

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−α, α>1. This has important cosmological consequences. In particular it leads to a relic gravitino density which becomes independent of the reheating temperature for TR>T∗. For small gravitino masses, m3/2⪡mg̃, the mass density of stable gravitinos is essentially determined by the gluino mass. The observed value of cold dark matter, ΩCDMh2∼0.1, is obtained for gluino masses mg̃=O(1 TeV).