Similarly, the “sneutrino D -term inflation” proposed in [661] assumed the sneutrino to be the inflaton. The superpotential is given by: W = λ M$_{P}$ N 2 $_{R}$Φ$_{+}$ $^{Φ}$− + λ$_{ν}$N$_{R}$H$_{u}$L + M$_{R}$ 2 N 2 R , (266) W = κS ( X$_{1}$X$_{2}$ − M 2 ) + λSH$_{u}$H$_{d}$ + ρ$_{ij}$ 2 SN$_{i}$N$_{j}$ + h ν $_{ij}$L$_{i}$ H$_{u}$N$_{j}$ + W ( µ =0) MSSM , (267) − L soft = M 2 $_{$_{S}$S}$∗$_{S}$ + ( κA$_{κ}$SX$_{1}$X$_{2}$ + λA$_{λ}$SH$_{u}$H$_{d}$ + ρ 2 A$_{ρ}$S ˜ N$_{i}$ ˜ N$_{i}$ − κa$_{S}$M $^{2}$S + H . c . ) , (268) 123 where N$_{R}$ is assumed to be the lightest right handed (s)neutrino, with U (1)$_{R}$ charge +1 and no U (1)$_{ξ}$ charge. Therefore, the tree level D -terms in the potential of Eq. (248) are not affected, though the additional couplings will affect the radiative correction, and therefore the dynamical properties of the model. Even with a minimal K¨ ahler potential, inflation is found to be successful in the regime, M 2 $_{R}$N$_{R}$ ≪ g 2 $_{ξ}$ξ $^{2}$. The model predicts an almost scale-invariant power spectrum, n$_{s}$ ≃ 1, and the constraint from the cosmic string tension is relaxed as compared to the standard case. There are also models where both F and D -terms are contributing to the inflationary potential. A mixture of the F - and D -term inflation was proposed by [662, 663], built as an extension to the NMSSM. The model is constructed in such a way that the inflaton field S involved in a F -term like superpotential also generates the µ term of the MSSM, and it is also coupled to the right-handed neutrinos, generating the Majorana mass scale. The symmetries of the model are also extended to G$_{S}$$_{M}$ × U (1)$_{ξ}$, the additional abelian factor allowing for the presence of a FI term. This subdominant contribution to the D -terms is employed to control the decay rate of superheavy fields such as the waterfall fields X$_{i}$ and the inflaton field into gravitinos. In this model, the potential is dominated by the F -terms. The renormalizable superpotential for the F$_{D}$ -terms hybrid model is given by: where W ( µ =0) MSSM denotes the MSSM superpotential without the µ -term, S is the SM-singlet inflaton superfield, N$_{i}$ are the right-handed Majorana neutrinos and X$_{1}$$_{,}$$_{2}$ is a chiral multi- plet pair with opposite charges under some U (1)$_{ξ}$ gauge group. Consequently, the D -term contribution to the scalar potential is given by: V$_{D}$ = ( g $^{2}$/ 8)( | X$_{1}$ | 2 − | X$_{2}$ | 2 − ξ ) $^{2}$. The soft SUSY-breaking sector can be obtained from Eq. (267) and reads: 5. F$_{D}$ -term hybrid inflation