4.4 “End of Inflation” Mechanism 99 Fig. 4.13: Prediction of the model for n ′ s for $^{φ}$∗ Case A with primordial inflation being Chaotic Inflation, with α =1 , Γ$_{ϕ}$ ≪ H$_{T I}$ , m$_{ψ}$ =10 − 2 GeV and the parameter values from Table 4.2. (A plot of Eq. (4.189), with $^{φ}$∗ = 〈 φ 〉 , m = m$_{0}$ and Γ= g $^{2}$m$_{0}$ .) The Blue line is the central value of n ′ s as obtained by the Planck spacecraft [40], with the lower and upper bounds being outside the displayed range of n ′ $_{s}$. In order for this and Eq. (4.165) to both be satisfied, we require the lower bound in Eq. (4.192) to be much smaller than the upper bound in Eq. (4.165). This gives We now require the lower bound here to be much smaller than the upper bound in Eq. (4.166). This gives where we have explicitly factored out the 1 (2 n +4)! term from our definition of λ . Given that n ≥ 1 , this constraint is in conflict with the requirement that λ ≲ 1 . Therefore, for α = 1 , we find that the “end of inflation” mecha- λ ≫ (2 n + 4)! 10 10 n +26 GeV 2 M 2 P (4.194) m$_{0}$ ≫ 10 8 GeV (4.193) 10 2 10 4 10 6 10 8 m 0 ( GeV ) - 0.0020 - - 0.0010 -$^{0.0000}$ n$_{s}$