in better agreement with experimental measurements, compared to the minimal Pati Salam model. The inflaton sector now relies on the following superpotential [70] W new shifted = κS (Φ ¯ Φ − M $^{2}$) − βS Ψ 2 + m Ψ ¯ Ψ + λ ¯ ΨΦ ¯ Φ , (242) which leads to the following F -term contribution to the scalar potential V = ∣ κ (Φ ¯ Φ − M $^{2}$) − β Ψ 2 ∣ $^{2}$+ ∣ 2 β Ψ − m ¯ Ψ ∣ $^{2}$+ ∣ m Ψ + λ Φ ¯ ∣ $^{2}$+ ∣ κS + λ ¯ Ψ ∣ 2 ( | Φ | 2 + ∣ ¯ Φ ∣ 2 ) , (243) The flat directions of the potential are at 〈 Φ 〉 = 〈 ¯ Φ 〉 = 〈 Ψ 〉 = 〈 ¯ Ψ 〉 = 0 for the trivial one, and at 〈 Φ 〉 = 〈 ¯ Φ 〉 = v , 〈 S 〉 > 0 , 〈 Ψ 〉 = − M 2 √ κ βξ , 〈 ¯ Ψ 〉 = − S κ λ , (244) where v 2 ≡ 2 κ $^{2}$(1 / 4 ξ + 1) + λ $^{2}$/ξ 2( κ 2 + λ $^{2}$) ξ. Inflation is assumed to take place in this shifted valley, and thus in this model breaking of the Pati-Salam group to the SM group (and the formation of monopoles associated with it) is realized during inflation. Indeed, the VEV of Φ breaks completely the Pati- Salam gauge group only leaving the SM group unbroken (the doublet of SU (2)$_{R}$ breaks it completely and the 4 of SU (4)$_{c}$ necessarily breaks its U $^{(1)$_{B}$}$− L subgroup [430]). The presence of many free parameters in this model only allows to confirm that with reasonable parameter values (coupling of order 10 − $^{2}$, and masses and unification scales around 10 $^{15}$− 10 16 GeV), the normalization to COBE, around 60 e-foldings of inflation, and a spectral index around n$_{s}$ ≃ 0 . 98 can be obtained [70]. The motivations and the mechanism behind the “new smooth hybrid inflation” [83] are identical, with a similar potential given by Eq. (242). The predictions of the model are: n$_{s}$ ≃ 0 . 969 , r ≃ 9 . 4 × 10 − 7 , α$_{s}$ ≃ − 5 . 8 × 10 − 4 [83]. A “semi-shifted hybrid inflation” was also proposed [84], with a similar framework of the extended Pati-Salam group, as for new shifted or new smooth hybrid inflation and the same (super)potential. In this model, however, the chosen inflationary valley is different, since it takes advantage of a third flat direction appearing only if ˜ M 2 ≡ 113