theory contains non-renormalizable terms and reads: where the spinors are denoted by: Φ , ¯ Φ , Φ ′ , ¯ Φ ′ and S,P,Z$_{1}$,Z$_{2}$ being the 4 gauge singlets. Plugging in the VEV required to achieve the symmetry breaking of SO(10) allows to identify which of the components of 16 + 16 stay light during inflation, and which are coupled to the GUT Higgs fields and thus acquire a GUT scale mass. This is important for the predictions of the F -term hybrid inflation model, since only the light states will contribute to the radiative corrections and to the effective N in front of the ln term (see Sec. IV E 2 and Eq. (222)). In this particular model, Φ is a 16-dimensional spinor, only two of its components will remain light, although having such light states is rather model dependent issue. Finally, an embedding of shifted hybrid inflation in a very elaborated SO (10) model has been proposed in [76], and an embedding of D -term hybrid model has been proposed in [66]. 4. Origin of a gauge singlet inflaton within SUSY GUTs It is desirable to seek an answer to the question, whether F -term hybrid inflation coupled or embedded within SUSY GUTs? Independently of the assumed GUT group, because of the form of the superpotential Eq. (219), the inflaton superfield, S , is necessarily an absolute gauge singlet , since SM 2 cannot be a gauge invariant if S is not an singlet superfield [691]. To fully embed the inflation model within SUSY GUTs, one could generate M by the VEV of some other field, though this has not yet been done so far, and attempts in this direction within the minimal SO (10) model of [441] are unsuccessful [691]. These models are based on a minimal number of superfields, and a protected R-parity at low energies. It contains only a Σ ≡ 210 , a pair Φ ≡ 126 , Φ ≡ 126 and a fundamental H = 10 , and the most general superpotential with this field content given by [441]: One can show that any VEV that would generate the mass term M 2 in the inflaton su- perpotential would also generate a mass for the inflaton field [691]. As a conclusion it is 135 W SO (10) min = m$_{Σ}$ Σ 2 + m$_{Φ}$ ΦΦ + λ$_{Σ}$ Σ 3 + η ΣΦΦ + m$_{H}$H 2 + Σ H ( α Φ + ¯ α Φ) . (293) W = S (Φ ¯ Φ − M $^{2}$) + α 4 M$_{S}$ A 4 + 1 2 M$_{A}$A 2 + T$_{1}$AT$_{2}$ + M$_{T}$T 2 + ¯ $_{Φ}$′ [ ζ PA M$_{S}$ + ζ$_{Z}$Z$_{1}$ ] Φ + ¯ Φ [ ξ PA M$_{S}$ + ξ$_{Z}$Z$_{1}$ ] $_{Φ}$′ + M$_{Φ}$ ¯ $_{Φ}$′$_{Φ}$ ′ . (292)