Cosmological moduli problem and oscillating inflation in gauge-mediated supersymmetry breaking

We investigate cosmological moduli problem in the gauge-mediated supersymmetry breaking (GMSB). A mini-inflation (oscillating inflation) takes place when a scalar field corresponding to the flat direction in GMSB oscillates along the logarithmic potential induced by the gauge-mediation mechanism. It is shown that this oscillating inflation can sufficiently dilute the relic abundance of the string moduli for some ranges of parameters in the GMSB models.