4.4 “End of Inflation” Mechanism 71 Combining the frozen value $^{ψ}$∗ , Eq. (4.92), with $^{ψ}$∗ ≫ $^{δψ}$∗ and δψ 2 α − 1 ∗ ∼ H 2 α − 1 ∗ gives The effective mass of φ at the end of primordial inflation is 4.4.3.6 Thermal Fluctuation of φ We have gT$_{end,inf}$ ≫ m$_{0}$ , which therefore gives The proof is as follows. Instead of considering the time of the end of primor- dial inflation, we consider the time at the start of thermal inflation, which is of course a time at a lower temperature. For the case Γ$_{ϕ}$ ≳ H$_{TI}$ , we would be saying that Substituting V$_{0}$ , Eq. (4.8), into Eq. (4.101) gives m 2 φ, end,inf ∼ g $^{2}$T 2 end,inf − m 2 0 (4.98) m$_{φ,}$$_{end,inf}$ ∼ g T$_{end,inf}$ (4.99) m$_{0}$ ≫ 100 h H α ∗ M α − 1 P (4.97) gT$_{1}$ ≫ m$_{0}$ (4.100) gV 1 4 0 ≫ m$_{0}$ (4.101) m$_{0}$ ≪ ( g 2 n +2 √$_{λ}$ ) 1 n M$_{P}$ (4.102)