4.4 “End of Inflation” Mechanism 80 we obtain The energy density of φ during primordial inflation is with the second line coming from Eq. (4.77) regarding the dynamics of ther- mal inflation. Therefore, with the energy density of the Universe being ∼ M 2 $_{P}$H 2 ∗ , we require and Substituting 〈 φ 〉 , Eq. (4.7), into Eq. (4.142) gives the same constraint as from substituting 〈 φ 〉 into Eq. (4.143). This constraint is However, for all viable parameter values in our model, this constraint is never the dominant constraint when we consider it alongside all of the other con- m$_{0}$ ≪ ( √$_{λ M}$$_{P}$$_{H}$ n +1 ∗ ) 1 n +2 (4.144) √$_{λ}$ 〈 φ 〉 n +2 ≪ M n +1 P $^{H}$∗ (4.143) m$_{0}$ 〈 φ 〉 ≪ M$_{P}$$^{H}$∗ (4.142) ρ$_{φ,}$$_{inf}$ = ( − 1 2 m 2 $_{0}$+ h 2 ψ 2 α ∗ M 2 α − 2 P ) 〈 φ 〉 $^{2}$+ λ 〈 φ 〉 2 n +4 M 2 n P (4.140) ∼ − 1 2 m 2 0 〈 φ 〉 $^{2}$+ λ 〈 φ 〉 2 n +4 M 2 n P (4.141) m$_{0}$ ≫ [ ( g $^{2}$Γ$_{ϕ}$ ) n +1 $^{√$_{λ M}$$_{P}$}$] 1 n +2 (4.139) $^{φ}$∗ Case A