content_image/347357.jpg content_image/347356.jpg
theory contains non-renormalizable terms and reads: 

<img src='content_image/347357.jpg'>

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]: 

<img src='content_image/347356.jpg'>

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 

