minimal K¨ ahler potential $^{66}$. Then the scalar potential reads V D − SUGRA tree = λ $^{2}$exp ( | $^{φ}$− | 2 + | φ$_{+}$ | 2 + | S | 2 M 2 P )[ | φ$_{+}$$^{φ}$− | 2 ( 1 + | S | 4 M 4 P ) + | φ$_{+}$S | 2 ( 1 + | $^{φ}$− | 4 M 4 P ) + | $^{φ}$−S | 2 ( 1 + | φ$_{+}$ | 4 M 4 P ) + 3 | $^{φ}$−φ$_{+}$S | 2 M 2 P ] + g 2 ξ 2 ( | φ$_{+}$ | 2 − | $^{φ}$− | 2 + ξ ) 2 , (248) where g$_{ξ}$ is the gauge coupling of U (1)$_{ξ}$. Here, we have assumed a minimal K¨ ahler potential K = | $^{φ}$− | 2 + | φ$_{+}$ | 2 + | S | $^{2}$. The global minimum of the potential is obtained for 〈 S 〉 = 0 and 〈 $^{Φ}$− 〉 = √$_{ξ}$$_{, which is SUSY preserving but induces the breaking of}$ U (1)$_{ξ}$. For S > S$_{inst}$ ≡ $_{g$_{ξ}$}$√$_{ξ/λ}$ the potential is minimized for | φ$_{+}$ | = | $^{φ}$− | = 0 and therefore, at the tree level, the potential exhibits a flat inflationary valley, with vacuum energy V$_{0}$ = g 2 $_{ξ}$ξ $^{2}$/ 2. The radiative corrections depend on the splitting between the effective masses of the components of the superfields Φ$_{+}$ $^{and Φ}$−, because of the transient D -term SUSY breaking. Extracting the quadratic terms from the potential Eq. (248), the scalar components φ$_{+}$ and $^{φ}$− get squared masses: while the squared mass of the Dirac fermions reads The radiative corrections are given by the Coleman-Weinberg expression [360] and the full potential inside the inflationary valley reads with Inflation ends when the slow-roll conditions break down, that is for z$_{end}$ ≃ 1, and the predictions for the inflationary parameters are very similar to the previous discussion on 66 This is the simplest SUGRA model and in general the K¨ ahler potential can be a more complicated function of the superfields. 116 m 2 ± = λ $^{2}$| S | $^{2}$exp ( | S | 2 M 2 Pl ) ± g 2 $_{ξ}$ξ , (249) m 2 f = λ $^{2}$| S | $^{2}$exp ( | S | 2 M 2 Pl ) . (250) V D − SUGRA eff = g 2 $_{ξ}$ξ 2 2 { 1+ g 2 ξ 16 π 2 [ 2 ln λ $^{2}$| S | 2 Λ 2 exp ( | S | 2 M 2 P ) + ( z + 1) $^{2}$ln(1 + $_{z}$− $^{1}$) + ( z − 1) $^{2}$ln(1 − $_{z}$− $^{1}$) ]} , (251) z = λ $^{2}$| S | 2 g 2 $_{ξ}$ξ exp ( | S | 2 M 2 P ) . (252)