4.4 “End of Inflation” Mechanism 84 where A is a constant and we are keeping only the growing mode. Therefore we have We know that and Therefore we have For all values of n , λ and m$_{0}$ , we have Δ t ≥ m − 1 0 . Therefore, from Eq. (4.153) we have Given that ζ ∼ 10 − $^{5}$, we require ln ( φ$_{2}$ φ$_{1}$ ) ∼ m$_{0}$ ( t$_{2}$ − t$_{1}$ ) (4.158) ∼ m$_{0}$ Δ t (4.159) φ$_{1}$ ∼ T ∼ m$_{0}$ (4.160) φ$_{2}$ ∼ 〈 φ 〉 (4.161) ln      1 √ (2 n + 4) λ ( M$_{P}$ m$_{0}$ ) n   1 n +1    ∼ m$_{0}$ Δ t (4.162) ζ ≫ H$_{TI}$ m$_{0}$ (4.163) H$_{TI}$ ≪ $_{10}$− $^{5}$m$_{0}$ (4.164)