4.4 “End of Inflation” Mechanism 96 In order to obtain n$_{s}$ and n ′ $_{s}$, we first need to obtain $^{N}$∗ . The prediction of the model for N$_{TI}$ and $^{N}$∗ are shown in Figs. 4.10 and 4.11 respectively, with n , g , $^{H}$∗ , Γ$_{ϕ}$ and λ values from Table 4.2. The kink that is visible in the plot of $^{N}$∗ at around m$_{0}$ ≈ 10 9 GeV is a result of the fact that for m$_{0}$ values larger than this, we do not have any period of thermal inflation, as can be seen in the plot of N$_{TI}$ . The values of N$_{TI}$ and $^{N}$∗ for a thermal waterfall field mass of m$_{0}$ ∼ 10 3 GeV are shown in Table 4.5. The prediction of the model for n$_{s}$ and n ′ s for each $^{φ}$∗ case and for a spectator field mass at the upper bound of m$_{ψ}$ = 10 − 2 GeV are shown in Fig. 4.10: Prediction of the model for N$_{TI}$ , with Γ$_{ϕ}$ ≪ H$_{T I}$ and n , g , Γ$_{ϕ}$ and λ values from Table 4.2. (A plot of Eq. (4.62), with m = m$_{0}$ .) Table 4.5: Prediction for N$_{TI}$ and $^{N}$∗ of the model, with Γ$_{ϕ}$ ≪ H$_{TI}$ , m$_{0}$ ∼ 10 3 GeV and n , g , $^{H}$∗ , Γ$_{ϕ}$ and λ values from Table 4.2. 10 2 10 4 10 ✁ 10 ✂ 10 10 m 0 ( GeV ) 0 10 20 N TI Parameter Value N$_{TI}$ ≈ 24 $^{N}$∗ 28