4.4 “End of Inflation” Mechanism 85 We obtain an additional constraint by substituting Eq. (4.164) into the requirement of m$_{ψ}$ ≪ H$_{TI}$ , Eq. (4.90). This gives A further constraint is obtained by substituting H$_{T I}$ , Eq. (4.10), into Eq. (4.164). We obtain As ψ has acquired perturbations from primordial inflation, we require it not to dominant the energy density of the Universe after the end of thermal infla- tion when it is oscillating, at which time the effective mass of ψ is increased significantly due to the coupling of ψ to φ . This is so as not to allow ψ to act as a curvaton, i.e. not to allow ψ ’s perturbations to generate a dominant contribution to the primordial curvature perturbation when ψ decays. The reason for this is just so that we do not have a curvaton inflation scenario, as the perturbations that are generated via the modulated mass in our model that could give the dominant contribution to ζ would be negligible. The energy density of the oscillating ψ field after the end of thermal 4.4.3.11 Energy Density of the Oscillating Spectator Field m$_{0}$ ≪ $_{10}$− 5 n − 5 √$_{λ M}$$_{P}$ (4.166) m$_{ψ}$ ≪ $_{10}$− $^{5}$m$_{0}$ (4.165)