Calculation of CWKB envelope in boson and fermion productions

We present the calculation of envelope of boson and of both low-and high-mass fermion production at the end of inflation when the coherently oscillating inflations decay into bosons and fermions. We consider three different models of inflation and use CWKB technique to calculate the envelope to understand the structure of resonance band formation. We observe that though low-mass fermion production is not effective in preheating because of Pauli blocking, it is quite probable for high-mass fermion to take part in pre heating. (author)