content_image/320633.jpg content_image/320634.jpg content_image/320635.jpg content_image/320636.jpg content_image/320637.jpg content_image/320632.jpg
where η is a slow-roll parameter given by 

<img src='content_image/320633.jpg'>

where V ′′ ( ϕ ) is the second derivative of the inflaton potential with respect to the inflaton field ϕ . η is to be evaluated at the point where cosmological scales exit the horizon during primordial inflation. By differentiating η$_{ψψ}$ with respect to N using the quotient rule, we obtain 

<img src='content_image/320634.jpg'>

<img src='content_image/320635.jpg'>

<img src='content_image/320636.jpg'>

<img src='content_image/320637.jpg'>

with the second line coming from the fact that we have V$_{ψψ}$ not depending on N , as we are assuming that both ψ and φ have settled to a constant value (Sections 4.4.3.5 and 4.4.3.8 respectively) by the time cosmological scales exit the horizon during primordial inflation. By differentiating the natural log of H with respect to N , we obtain [1] 

<img src='content_image/320632.jpg'>

