content_image/326259.jpg content_image/326260.jpg content_image/326261.jpg content_image/326262.jpg content_image/326263.jpg content_image/326264.jpg
Substituting these equations into Eq. (B.9) gives 

<img src='content_image/326259.jpg'>

The argument of the delta function is only =0 if p ′ = p . Therefore we have 

We have 

<img src='content_image/326260.jpg'>

<img src='content_image/326261.jpg'>

From the 4-momenta of p$_{2}$ , Eq. (B.2), we know that E$_{2}$ = p . In addition, given that the energy of a χ particle is T , we therefore have 

Let us consider the time of primordial inflation reheating. We have 

Therefore 

<img src='content_image/326262.jpg'>

<img src='content_image/326263.jpg'>

<img src='content_image/326264.jpg'>

