Cosmological Constraint on the String Dilaton in Gauge-Mediated Supersymmetry Breaking Theories

The dilaton field in string theories (if it exists) is expected to have a mass of the order of the gravitino mass $m_{3/2}$ which is in a range of ${10}^{-2\mathrm{}}\mathrm{keV}–1\mathrm{GeV}$ in gauge-mediated supersymmetry breaking models. If this is the case, the cosmic energy density of coherent dilaton oscillation easily exceeds the critical density of the present Universe. We show that even if this problem is solved by a late-time entropy production (thermal inflation) a stringent constraint on the energy density of the dilaton oscillation is derived from experimental upper bounds on the cosmic x( $\gamma$)-ray backgrounds. This excludes an interesting mass region, $500\mathrm{keV}\lesssim m_{3/2}\lesssim 1\mathrm{GeV}$, in gauge-mediated supersymmetry breaking models.