SUSY breaking and non-renormalizable superpotential terms of the type [91, 92] W$_{non}$ = ∑ n> 3 λ$_{n}$ n Φ n M n − 3 , (310) are included. Here Φ is a gauge invariant superfield which contains the flat direction. Within MSSM all the flat directions are lifted by non-renormalizable operators with 4 ≤ n ≤ 9 [407], where n depends on the flat direction. Let us focus on the lowest order superpotential term in Eq. (310) which lifts the flat direction. Softly broken SUSY induces a mass term for φ and an A -term so that the scalar potential along the flat direction reads [87, 88] V = 1 2 m 2 φ φ 2 + A cos( nθ + θ$_{A}$ ) λ$_{n}$φ n n M n − 3 P + λ 2 n φ 2( n − 1) M 2( n − 3) P , (311) Here φ and θ denote respectively the radial and the angular coordinates of the complex scalar field Φ = φ exp[ iθ ], while θ$_{A}$ is the phase of the A -term (thus A is a positive quantity with dimension of mass). Note that the first and third terms in Eq. (311) are positive definite, while the A -term leads to a negative contribution along the directions whenever cos( nθ + θ$_{A}$ ) < 0. As discussed in [87–90], among nearly 300 flat directions [407], there are two that can lead to a successful inflation along the lines discussed above. One is udd , up to an overall phase factor, which is parameterized by: 1. Inflaton candidates Here 1 ≤ α, β, γ ≤ 3 are color indices, and 1 ≤ i, j, k ≤ 3 denote the quark families. The flatness constraints require that α = β = γ and j = k . The other direction is LLe , parameterized by (again up to an overall phase factor) u α i = 1 √$_{3}$ φ , d β j = 1 √$_{3}$ φ , d γ k = 1 √$_{3}$ φ . (312) L a i = 1 √$_{3}$   0 φ   , L b j = 1 √$_{3}$   φ 0   , e$_{k}$ = 1 √$_{3}$ φ , (313) where 1 ≤ a, b ≤ 2 are the weak isospin indices and 1 ≤ i, j, k ≤ 3 denote the lepton families. The flatness constraints require that a = b and i = j = k . Both these flat directions are lifted by n = 6 non-renormalizable operators [407], W$_{6}$ ⊃ 1 M 3 P ( LLe )( LLe ) , W$_{6}$ ⊃ 1 M 3 P ( udd )( udd ) . (314) 145