  Particle production caused by the oscillation after inflation is important
since it explains reheating after inflation. On the particle theory side, we
know that effective action may have additional higher dimensional terms
(usually called non-renormalizable terms) suppressed by the cut-off scale.
Moreover, interaction between inflaton and so-called moduli field will be
higher dimensional. Therefore, if such higher dimensional interaction is
significant for resonant particle production, one cannot avoid the effect in
preheating study. We explicitly calculated the required number of oscillation
for the energy transfer. Consequently, cosmological history of an oscillating
field and the moduli problem can be reconsidered.
