content_image/301514.jpg content_image/301515.jpg content_image/301516.jpg content_image/301513.jpg content_image/301517.jpg content_image/301518.jpg
We obtain an expression for $^{ϕ}$∗ in terms of $^{N}$∗ by using the equation 

<img src='content_image/301514.jpg'>

We define the end of primordial inflation to be when ϵ =1 . This gives 

Therefore we have 

Substituting Eq. (4.181) into Eq. (4.176) gives 

<img src='content_image/301515.jpg'>

<img src='content_image/301516.jpg'>

<img src='content_image/301513.jpg'>

<img src='content_image/301517.jpg'>

We also need to calculate η$_{ψψ}$ . Using our potential, Eq. (4.2), we obtain V$_{ψψ}$ at the time cosmological scales exit the horizon as 

<img src='content_image/301518.jpg'>

