4.4 “End of Inflation” Mechanism 76 to the start of thermal inflation. Therefore we have the constraint Taking Eq. (4.121) with T ∼ ( M 2 P $^{H}$∗ Γ$_{ϕ}$) 1 4 gives We also require Γ$_{therm}$ > H to be satisfied throughout the whole of thermal inflation. Therefore, we have the constraint Substituting H$_{TI}$ and T$_{2}$ , Eqs. (4.10) and (4.13) respectively, into the above gives We consider three possible cases for the value of the thermal waterfall field φ during primordial inflation, with m$_{φ,}$$_{inf}$ being the effective mass of φ during primordial inflation: 4.4.3.8 The Field Value $^{φ}$∗ m$_{0}$ < ( g 3 √$_{2}$ ) n +1 √$_{λM}$$_{P}$ (4.125) g $^{4}$T$_{2}$ > H$_{TI}$ (4.124) Γ$_{therm}$ $^{> H}$∗ (4.122) Γ$_{ϕ}$ > H 3 ∗ g $^{16}$M 2 P (4.123) A) φ heavy, i.e. | m$_{φ,}$$_{inf}$ | ≫ $^{H}$∗ , in which φ rolls down to its VEV. B) φ light, i.e. | m$_{φ,}$$_{inf}$ | ≪ $^{H}$∗ , in which φ is at the Bunch-Davies value (to be explained below). C) φ light, in which a SUGRA correction to the potential is appreciable,