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can also be involved in the see-saw mechanism. Assuming an SO (10) model that preserves the R-parity, and using a minimum number of fields to realize this breaking, this is realized generically employing a pair Φ = 126 , Φ = 126 [445], though Φ = 16 , Φ = 16 is also possible, and does not preserve the R-parity. Since the U $^{(1)$_{B}$}$− L symmetry breaking scale is also commonly used to generate the Majorana mass for right-handed neutrinos, this opens up the possibility to combine constraints from neutrino measurement and CMB constraints on the parameter space in specific models with these ingredients. 

## 3. Embedding inflation within GUT 

Several embeddings of F -term models of inflation in a specific and realistic SUSY GUT model have been proposed, see Refs [73, 76, 690, 691]. Most of these references [73, 76, 690] have considered SUSY SO (10) models that are capable of accounting for enough proton stability, a (semi-)realistic mass matrix for fermions, and a doublet-triplet (D-T) splitting usually through the Dimopoulos-Wilczek mechanism. We will discuss such models in this section and also discuss a more minimal model of SO (10) [691] in the next subsection. 

Imposing that the R-parity is unbroken at low energy is usually assumed in order to pro- tect the proton from a too rapid decay through dimension 4 operators involving sparticles (see Sec. III F). SO (10) contains a Z$_{2}$ symmetry subgroup of U $^{(1)$_{B}$}$− L ⊂ SU (4)$_{C}$ ⊂ SO (10) that can play this role provided only “safe” Higgs representations are employed to re- alize SO (10) → G$_{S}$$_{M}$ , namely via 10 , 45 , 54 , 126 , 126 , 210 , etc. Therefore, in Ref. [690], the model has the following field content; two pairs of adjoint 45 and 54 denoted A$_{45}$,A ′ $_{45}$,S$_{54}$ ,S ′ 54 are assumed to break SO (10) down to 3$_{c}$2$_{L}$1$_{R}$$^{1$_{B}$}$− L while a pair 126 + 126 denoted Φ + ¯ Φ is used to break the B − L symmetry and obtain the MSSM G$_{S}$$_{M}$ × Z R 2 . An additional pair ( H,H ′ ) of fundamental 10 are assumed for the electroweak symmetry breaking and one last 45 denoted A ′′ is also required to avoid dangerous light degrees of freedom. 

Finally F -term hybrid inflation is realized adding an SO (10) singlet S to this field con- tent. The superpotential then contains 5 sectors, the first two implementing the breaking of SO (10) and the electroweak symmetry breaking respectively, and the D-T splitting at the same time, [690] 

<img src='content_image/341508.jpg'>

