not possible to generate exactly the F -term model, at least within this minimal version of SO (10). 

Another concerning issue is the stability of the superpotential [691]. The form of the superpotential of Eq. (219) is supposedly protected by a U (1)$_{R}$ symmetry, under which S is doubly charged, while Φ and Φ have opposite charges. This property is important for example to prevent contributions to W such as quadratic or cubic terms in the inflaton superfield, that would spoil the flatness of the inflationary potential. Furthermore, assigning R -charges to obtain flatness of the inflaton potential in presence of the Higgs sector is also challenging. For example, the minimal SO (10) model of [441], whose most general superpotential cannot be invariant under such an R -symmetry. Trying to accommodate a phase of F -term inflation in such model would receive destabilization from various sources. 

• Quadratic and cubic terms in the inflaton potential, which would a-priori ruin the flatness of the potential. It is possible to arrange the parameters to realize a saddle point or an inflection point inflation. More work is required in this direction. 

• Additional couplings between the inflaton, S , and other singlets (including S Φ 2 i for all the superfields Φ$_{i}$ in the theory), which would demand additional assumptions such that these Φ$_{i}$ superfields remain heavy during inflation via their couplings. 

• Like the original hybrid model, those additional couplings would generate dangerous quadratic and cubic terms at one-loop level, even if they were assumed vanishing at the tree level. One would have to ensure that extra terms do not spoil the flatness of the potential. 

Note that these stability problems are also present in earlier attempts to embed F -term hybrid inflation in SUSY GUTs. If these stability issues are left aside, it is interesting to note that among all possible global minima of the minimal SO (10) theory, one and only one of them can accommodate a phase of F -term inflation, when the stability of the potential against VEV shifting and the formation of topological defect formation are taken into account [691]. 

