Cosmological moduli problem in gauge-mediated supersymmetry breaking theories

A generic class of string theories predicts the existence of light moduli fields, and they are expected to have masses $m_{\phi }$ comparable to the gravitino mass $m_{3/2}$ 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 ${10}^{-2}$ keV$\lesssim m_{3/2}\lesssim 1$ 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 ${10}^{-2}$ keV$\lesssim m_{3/2}\lesssim 500$ keV to survive the constraints. It is also stressed that the moduli can be dark matter in our universe for the mass region ${10}^{-2}$ keV$\lesssim m_{\phi }\lesssim 100$ keV.