4.3 φ Decay Rate, Spectral Index and Tensor Fraction 53 where ϵ$_{H}$ and η$_{ψψ}$ are slow-roll parameters, defined as 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 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 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 n$_{s}$ ≃ 1 − 2 ϵ + 2 η$_{ψψ}$ (4.23) ϵ ≡ M 2 P 2 ( V ′ ( ϕ ) V ( ϕ ) ) 2 (4.22) ϵ$_{H}$ ≡ 2 M 2 P ( H ′ ( ϕ ) H ( ϕ ) ) 2 (4.20) η$_{ψψ}$ ≡ V$_{ψψ}$ 3 H 2 (4.21) and