4.4 “End of Inflation” Mechanism 67 scenario for the trajectory. It is not a requirement on the model itself. In or- der that the ψ field does not affect the inflationary trajectory during thermal inflation, we require from our m mass definition, Eq. (4.3), Therefore we have From our potential, Eq. (4.2), Eq. (4.77) gives For Γ$_{ϕ}$ ≳ H$_{TI}$ , substituting T$_{1}$ from Eq. (4.11) into Eq. (4.79) gives and for Γ$_{ϕ}$ ≪ H$_{TI}$ , substituting T$_{1}$ from Eq. (4.12) into Eq. (4.79) gives Given that we have not observed any φ particles, the most liberal constraint on the present value of the effective mass of φ is 4.4.3.3 Lack of Observation of φ Particles m$_{0}$ ≫ h ψ α M α − 1 P (4.77) m ≃ m$_{0}$ (4.78) m 2 0 < 2 g $^{2}$T 2 1 (4.79) m$_{0}$ < ( g 2 n +2 √$_{λ}$ ) 1 n M$_{P}$ (4.80) m$_{0}$ < [ ( g $^{4}$Γ$_{ϕ}$ ) n +1 M 2 n +1 P √$_{λ}$ ] 1 3 n +2 (4.81) m$_{φ,}$$_{now}$ ≳ 1 TeV (4.82)