content_image/314224.jpg content_image/314225.jpg content_image/314223.jpg content_image/314222.jpg
where ϵ$_{H}$ and η$_{ψψ}$ are slow-roll parameters, defined as 

and 

<img src='content_image/314224.jpg'>

<img src='content_image/314225.jpg'>

where H ′ ( ϕ ) is the derivative of the Hubble parameter with respect to the inflaton field ϕ and V$_{ψψ}$ ≡ ∂ $^{2}$V ∂ψ $_{2}$. ϵ$_{H}$ and η$_{ψψ}$ are to be evaluated at the point where cosmological scales exit the horizon during primordial inflation. In the limit of slow-roll inflation, which we consider to be the case for our primordial inflation period, ϵ$_{H}$ → ϵ , which is defined as 

<img src='content_image/314223.jpg'>

where V ( ϕ ) is the inflaton potential and V ′ ( ϕ ) is the derivative of that po- tential with respect to the inflaton field ϕ . ϵ is to be evaluated at the point where cosmological scales exit the horizon during primordial inflation. The spectral index now becomes 

<img src='content_image/314222.jpg'>

Regarding the various scalar fields involved in this model, the reason why ϵ depends only on ϕ is because this slow-roll parameter captures the infla- tionary dynamics of primordial inflation, which is governed only by ϕ in our model (we are assuming that both ψ and φ have settled to a constant value 

