and a negligible running spectral index. • Shifted hybrid inflation: The shifted inflation model is similar to the smooth model except that the additional Z$_{2}$ symmetry is not imposed. As a consequence, the superpotential reads [67] W shifted = κS [ ¯ ΦΦ − M 2 ] − β S ( ¯ ΦΦ) 2 M 2 P , (236) where Φ , ¯ Φ are two distinct superfields that belong to non-trivial representations of the Pati-Salam group G$_{P}$$_{S}$ = SU (4)$_{c}$ × SU (2)$_{L}$ × SU (2)$_{R}$: Φ ∈ ( ¯ 4 , 1 , 2 ), ¯ Φ ∈ ( 4 , 1 , 2 ). This gives rise to the following F -terms (in global SUSY) Following [68], we define the relevant fields ¯ φ and φ as the component of ¯ Φ and Φ that generates the symmetry breaking G$_{P}$$_{S}$ → G$_{S}$$_{M}$ , that is to give a VEV to a component of Φ that is charged under G$_{P}$$_{S}$ but not under G$_{S}$$_{M}$ . For the inflaton field, we will define s ≡ | S | . We can also choose to set β > 0 and ¯ φ ∗ = φ , so that the potential is D -flat and becomes The second form is for normalized fields, w = s/M , y = φ/M and ξ ≡ βM $^{2}$/κM$_{S}$ . The potential is represented by Fig. (6). We can observe that the potential contains three (respectively two) local minima at high (respectively small ) values of the inflaton field w , if ξ ≥ 1 / 4 is of the order of unity (Fig. (6) left). They are located at y = 0 for the central one while the other valleys are “shifted” away from y = 0, with a trajectory function of the inflaton field y = f ( w ). The number of valleys goes up to four at small inflaton VEVs and intermediate values of 1 / 7 . 2 < ξ < 1 / 4 (Fig. (6) right): two new shifted valley at y = ± 1 $_{/}$√$_{2}$$_{ξ}$ appears. At smaller values of ξ , both shifted valleys become indistinguishable. If inflation is 109 V $^{shifted}$( s, φ ) = κ 2 [ − M 2 + | φ | 2 − β κM 2 $_{P}$| φ | 4 ] 2 + 2 κ $^{2}$s$^{2}$| φ | 2 [ 1 − 2 β κM 2 $_{P}$| φ | 2 ] 2 , V $^{shifted}$( w, y ) κ $^{2}$M4 = ( y 2 − 1 − ξy $^{4}$)2 + 2 w $^{2}$y$^{2}$(1 − 2 ξy $^{2}$)2 . (238)