content_image/373999.jpg content_image/374003.jpg content_image/374004.jpg
physics point of view $^{58}$. 

## 2. Hybrid inflation from F -terms 

The most well-known model of SUSY inflation driven by F -terms is of the hybrid type and based on the superpotential [62] 

<img src='content_image/373999.jpg'>

where, S is an absolute gauge singlet while Φ and Φ are two distinct superfields belonging to complex conjugate representation, and κ is an arbitrary constant fixed by the CMB ob- servations $^{59}$. This form of potential is protected from additional destabilizing contributions with higher power of S , if S , Φ and Φ carrying respectively the charges +2, α and − α under R-parity. Then W carries a charge +2 so that the action S = ∫ d $^{2}$θ W + . . . is invariant. The tree level scalar potential derived from Eq. (219) reads 

<img src='content_image/374003.jpg'>

where we have denoted by S, φ, φ the scalar components of S, Φ , Φ. It has a form similar to the original hybrid inflation model, though m = 0, and both λ and λ ′ are replaced by only one coupling constant κ $^{2}$. In what follows, it is assumed that φ ∗ = φ along this direction, the D -terms vanish and that the kinetic terms for the superfields are minimal, which is equivalent to a minimal K¨ ahler potential, K = | S | 2 + | Φ | 2 + | Φ | $^{2}$. 

We can defined two effective real scalar fields canonically normalized, σ ≡ √$_{2Re(}$$_{S}$$_{), and}$ ψ ≡ 2Re(Φ) = 2Re(Φ). The two-field scalar potential can then be put to the form [611] 

<img src='content_image/374004.jpg'>

Like in the non-SUSY version, the global minimum of the potential is located at S = 0, φφ = M $^{2}$, though at large VEVs, S > S$_{c}$ ≡ M , the potential also possesses a local valley of 

