4.5 Modulated Decay Rate 105 4.5.2.2 Light ψ For the “end of inflation” mechanism scenario, we required the effective mass of ψ to be light all the way up until the end of thermal inflation. However, in this modulated decay rate scenario, we require the effective mass to be light for longer, all the way up until φ decays, in order that ψ does not start oscillating, so that the perturbations in ψ remain at decay time and thus have the effect of perturbing the decay rate. Therefore we require We have Therefore we require and The φ field decays when H falls to ∼ Γ . Therefore we require | m$_{ψ,}$$_{eff}$ | ≪ H (4.204) | m$_{ψ,}$$_{eff}$ | ≪ Γ (4.205) m 2 ψ, eff = m 2 ψ + ( 4 α 2 − 2 α ) h $^{2}$φ2 ( ψ M$_{P}$ ) 2 α − 2 (4.206) m$_{ψ}$ ≪ Γ (4.207) hφ ( $^{ψ}$∗ M$_{P}$ ) α − 1 ≪ Γ (4.208) h 〈 φ 〉 ( $^{ψ}$∗ M$_{P}$ ) α − 1 ≪ Γ (4.209)