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enough to the inflationary valley. Note that in this reference, the radiative corrections to the inflationary potential has been approximated by a mass term, similarly to the non-SUSY case (see Sec. IV C). This model has been studied more recently with a high precision, taking into account of the SUGRA corrections induced by a minimal K¨ ahler potential [516]. 

In [516], the space of successful initial conditions is found composed of a non-fractal set of successful points but with fractal boundaries. Such a set is represented in Fig. (5), where for given initial VEVs, the number of e-foldings of inflation realized is represented. It was pointed out that similar to non-SUSY hybrid inflation, inflation is realized generically by a first phase of fast roll down the potential and when the velocity vector is correctly oriented at the bottom of the potential, the inflaton climbs up and slow-rolls back down the inflationary valley around 〈 ψ 〉 = 0. 

## 7. Other hybrid models and effects of non-renormalizable terms 

The superpotential of F -term hybrid inflation given in Eq. (219) contains only renormal- izable terms. However VEVs close to the UV cutoff of the theory, (necessarily smaller than the reduced Planck mass), non-renormalizable terms play a non-negligible role. Two mod- els have been proposed to study these effects: the “smooth” [63] and “shifted” [67] hybrid inflation models. 

The initial motivation for both of these models was to implement hybrid inflation in a GUT model based on the Pati-Salam gauge group G$_{P}$$_{S}$ ≡ SU (4)$_{C}$ × SU (2)$_{L}$ × SU (2)$_{R}$ without the formation of monopoles at the end of inflation. The idea is therefore to break the symmetry before the phase of inflation, which can be achieved by introducing one non- renormalizable term in the superpotential. 

• Smooth hybrid inflation: 

In this model [63], the superpotential has to satisfy a new Z$_{2}$ symmetry in addition to the R-symmetry and G$_{GUT}$ under which the pair of Higgs superfields would transform following Φ ¯ Φ → − Φ ¯ Φ. This forbids the second term in the superpotential of standard F -term inflation Eq. (219), but allows one of the first non-renormalizable term 

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