A generic class of string theories predicts the existence of light moduli fields, and they are expected to have masses m_φ comparable to the gravitino mass m3/2 which is in a range of 10^-2 keV to 1 GeV in gauge-mediated supersymmetry breaking theories. Such light fields with weak interactions suppressed by the Planck scale cannot avoid some stringent cosmological constraints; that is, they suffer from ``cosmological moduli problems.'' We show that the total gravitino mass region 10^-2 keVm3/21 GeV is excluded by the constraints even if we incorporate late-time mini-inflation (thermal inflation). However, a modification of the original thermal inflation model enables the region 10^-2 keVm3/2500 keV to survive the constraints. It is also stressed that the moduli can be dark matter in our universe for the mass region 10^-2 keVm_φ100 keV.
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Asaka et al. (1998) studied this question.
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