content_image/306807.jpg content_image/306808.jpg
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. 

<img src='content_image/306807.jpg'>

<img src='content_image/306808.jpg'>

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 

