content_image/315009.jpg content_image/315010.jpg content_image/315008.jpg content_image/315007.jpg content_image/315006.jpg content_image/315011.jpg
Therefore we obtain η$_{ψψ}$ as 

Our final result for the spectral index is therefore 

<img src='content_image/315009.jpg'>

<img src='content_image/315010.jpg'>

From Section 4.3.2, the running of the spectral index n ′ s is given by 

<img src='content_image/315008.jpg'>

with η being given by Eq. (4.29), which is to be evaluated at the point where cosmological scales exit the horizon during primordial inflation. The potential of Eq. (4.174) gives 

<img src='content_image/315007.jpg'>

which is identical to the value of ϵ , Eq. (4.176). Substituting Eq. (4.181) into Eq. (4.187) gives 

Our final result for the running of the spectral index is therefore 

<img src='content_image/315006.jpg'>

<img src='content_image/315011.jpg'>

