The mutated hybrid inflation is one of them with a potential of the form of Eq. (179) with ( p, q ) = (1 , 2) [528] V $^{mut}$( φ, ψ ) = 1 2 m $^{2}$( ψ − M ) 2 + λ 4 φ $^{2}$ψ2 . (180) Inflation in this case always happens for sub-Planckian VEVs. If one assumes chaotic initial values φ ≫ ψ , like for hybrid inflation, the potential is minimized at ψ = 0. While φ slow- rolls to smaller values, ψ settles in the local minimum satisfying, ψ = Mα ( φ ) / [1 + α ( φ )], with α ( φ ) = 2 m $^{2}$/ ( λφ $^{2}$). At large φ , α ≪ 1, and its effective potential is of the form of Eq. (175), with n = 2: V mut eff ≃ 1 2 m $^{2}$M2 ( 1 − 2 m 2 λφ 2 ) + O [ α $^{2}$( φ )] , (181) while the kinetic terms, though modified, are close to minimal. In this approximation, the model predicts a red spectral index and negligible tensor to scalar ratio, if we assume N$_{Q}$ ≃ 60. It is worth noting also that the model can emerge from a SUSY theory, e.g., from a superpotential of the form [528] f (Ψ) should be generated by non-perturbative process, such as gaugino condensation [31] in some hidden sector, in order to generate a Λ much smaller than the Planck scale. It also needs to satisfy f (0) = 1 and f ′ (0) < 0. The smooth hybrid inflation model [63] also belongs to the similar class of model, with a potential of the form of Eq. (179) with ( p, q ) = (4 , 6). It therefore involves non- renormalizable terms of order $_{M}$− 2 P . This model is also characterized by a φ -dependent minimum for ψ and, therefore a realization of inflation along a multi-field trajectory. The motivation presented in [63] is to avoid the formation of topological defects since the sym- metry breaking occurs during inflation when all topological defects are inflated away. This is necessary when the symmetry breaking gives rise to monopoles or domain walls. Along the inflationary trajectory, the effective one-field potential is of the form of Eq. (175), with n = 4. The end of slow-roll inflation in this model is necessarily triggered by a violation of 85 n$_{s}$ − 1 ≃ − 3 8 N$_{Q}$ ≃ 0 . 97 , r ≃ 3 m 2 λN 3 / 2 Q ≪ 3 8 N 2 Q ∼ $_{10}$− 4 , (182) W = Λ $^{2}$f (Ψ)Σ$_{1}$ + λ ΦΨΣ$_{2}$ . (183)