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. 
T. Asaka, M. Kawasaki, and Masahide Yamaguchi