4.3 φ Decay Rate, Spectral Index and Tensor Fraction 51 T$_{1}$ corresponds to the temperature when the potential energy density becomes comparable with the energy density of the thermal bath, for which the density is ρ$_{γ}$ ∼ T $^{4}$. In the case of Γ$_{ϕ}$ ≪ H$_{TI}$ , thermal inflation will begin at a temperature In both cases, thermal inflation ends at a temperature T$_{2}$ corresponds to the temperature when the tachyonic mass term of the thermal waterfall field becomes equal to the thermally-induced mass term in Eq. (4.5). The decay rate of φ is given by 4.3 φ Decay Rate, Spectral Index and Tensor Fraction 4.3.1 φ Decay Rate T$_{1}$ ∼ ( M 2 P H$_{TI}$ Γ$_{ϕ}$ ) 1 4 (4.12) T$_{2}$ = m √$_{2}$$_{g}$ (4.13) Γ ∼ max { g $^{2}$m$_{φ,}$$_{osc}$ , m 3 φ, osc M 2 P } (4.14)