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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 TT_*, which depends on the supersymmetry breaking mass scales, gauge couplings decrease like T^{-\a}, \a > 1. This has important cosmological consequences. In particular it leads to a relic gravitino density which becomes independent of the reheating temperature for TR>TT_R > T_*. For small gravitino masses, m_{3/2} \ll m_{\gl}, the mass density of stable gravitinos is essentially determined by the gluino mass. The observed value of cold dark matter, \O_{\rm CDM}h^2 \sim 0.1, is obtained for gluino masses m_{\gl} = {\cal O}(1 {\rm TeV}).Comment: 11 pages, 2 figures, comment on supersymmetry breaking mechanisms and two references adde

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