Constraints on Hybrid Inflation from Flat Directions in Supersymmetry
  We examine the constraints on F-term hybrid inflation by considering the flat directions in the Minimal Supersymmetric Standard Model (MSSM). We find that some coupling terms between the flat direction fields and the field which dominates the energy density during inflation are quite dangerous and can cause the no-exit of hybrid inflation even if their coupling strength is suppressed by Planck scale. Such couplings must be forbidden by imposing some symmetry for a successful F-term hybrid inflation. At the same time, we find that in the D-term inflation these couplings can be avoided naturally. Further, given the tachyonic preheating, we discuss the feasibility of Affleck-Dine baryogenesis after the F-term and D-term inflations. 
Fuqiang Xu, Jin Min Yang