where α 2 ≪ 1, there exists a point of inflection in V ( φ ) From now on we only keep the leading order terms in all expressions. Note that in gravity- mediated SUSY breaking, the A -term and the soft SUSY breaking mass are of the same order of magnitude as the gravitino mass, i.e. m$_{φ}$ ∼ A ∼ m$_{3}$$_{/}$$_{2}$ ∼ (100 GeV − 1 TeV). Therefore the condition in Eq. (318) can indeed be satisfied. We then have φ$_{0}$ ∼ O (10 14 GeV). Inflation occurs within an interval in the vicinity of the point of inflection, within which the slow-roll parameters ϵ ≡ ( M 2 $_{P}$/ 2)( V ′ /V ) 2 and η ≡ M 2 $_{P}$( V ′′ /V ) are smaller than 1. The Hubble expansion rate during inflation is given by The amplitude of density perturbations δ$_{H}$ and the scalar spectral index n$_{s}$ are given by [87, 88, 711, 712]: N$_{Q}$ is the number of e-foldings between the time when the observationally relevant perturba- tions are generated till the end of inflation and follows: N$_{Q}$ ≃ 66 . 9 + (1 / 4)ln( V ( φ$_{0}$ ) /M 4 $_{P}$) ∼ respectively where and 147 at which φ$_{0}$ = ( m$_{φ}$M 3 P $_{λ}$√$_{10}$ ) 1 / 4 + O ( α $^{2}$) , (319) $_{V}$′′$_{(}$$_{φ}$$_{0}$$_{) = 0}$$_{,}$ (320) V ( φ$_{0}$ ) = 4 15 m 2 $_{φ}$φ 2 0 + O ( α $^{2}$) , (321) V ′$_{(}$$_{φ}$$_{0}$$_{) = 4}$$_{α}$ $^{2}$m2 $_{φ}$φ$_{0}$ + O ( α $^{4}$) , (322) V ′′′$_{(}$$_{φ}$$_{0}$$_{) = 32}$ m 2 φ φ$_{0}$ + O ( α $^{2}$) . (323) | φ − φ$_{0}$ | ∼ φ 3 0 60 M 2 P , (324) H$_{MSSM}$ ≃ 1 √$_{45}$ m$_{φ}$φ$_{0}$ M$_{P}$ ∼ (100 MeV − 1 GeV) . (325) δ$_{H}$ = 8 √$_{5}$$_{π}$ m$_{φ}$M$_{P}$ φ 2 0 1 Δ 2 sin $^{2}$[ $_{N$_{Q}$}$√$_{Δ}$ $^{2}$] , (326) n$_{s}$ = 1 − $_{4}$√$_{Δ}$ 2 cot[ $_{N$_{Q}$}$√$_{Δ}$ $^{2}$] , (327) Δ 2 ≡ 900 α $^{2}$N − 2 Q ( M$_{P}$ φ$_{0}$ ) $^{4}$. (328)