Restriction to Parametric Resonant Decay after Inflation
  We study parametric resonant decay of inflaton field with emphasis on its physical meaning. We show that the parametric resonance is indeed an induced process, which means that the more numbers of produced particles, the more inflaton field decays. We also consider the dissipative effects of produced particles and find that the dissipation reduces the resonant decay rate of inflaton field. 
Shinta Kasuya and Masahiro Kawasaki