4.3 φ Decay Rate, Spectral Index and Tensor Fraction 52 where m$_{φ,}$$_{osc}$ is the effective mass of φ during the time of φ ’s oscillations around its VEV after the end of thermal inflation. This is calculated as Therefore we obtain The first expression is for decay into the thermal bath via direct interactions and the second is for gravitational decay. We will only consider the case in which the direct decay is the dominant channel ( g is not taken to be very small). This is the case when Thermal Inflation has the effect of changing the number of e-folds before the end of primordial inflation at which cosmological scales exit the horizon. This affects the value of the spectral index n$_{s}$ of the curvature perturbation ζ , assuming ζ is generated due to the perturbations of the spectator scalar field. The spectral index is given by [1] Therefore we have just 4.3.2 Spectral Index — n$_{s}$ and n ′ s n$_{s}$ ≃ 1 − 2 ϵ$_{H}$ + 2 η$_{ψψ}$ (4.19) Γ ∼ g $^{2}$m (4.18) m ≪ gM$_{P}$ (4.17) Γ ∼ max { g $^{2}$m , m 3 M 2 $_{P}$} (4.16) m$_{φ,}$$_{osc}$ ∼ m (4.15)