Along the D -flat direction, the VEVs are φ$_{1}$ = φ$_{2}$ = φ$_{3}$ ≪ M ≪ M$_{P}$ . One can further make an assumption such that κ$_{3}$ < − 1 / 3, so that the S field becomes heavy compared to the Hubble expansion rate, and therefore the field relaxes to its minimum VEV, S = 0, within one e-folding. By assuming | φ$_{i}$ | = $_{ϕ/}$√$_{2,}$ β = ( κ$_{2}$ − 1), λ = ( β ( β + 1) + 1 / 2 + κ$_{1}$/ 12) and γ = 2 / (6) 3 n/ 2 < ∼ 0 . 14, the potential along ϕ is given by [85] V ≃ µ 4 [ 1 − β 2 ϕ 2 M 2 P + λ 4 ϕ 4 M 4 P − γ ϕ 3 n M 3 n + · · · ] . (306) One needs to suppress the quartic term in the potential, i.e. ϕ 4 term, otherwise for | γϕ 3 $^{n}$/M 3 $^{n}$|  ≪ | ( λ/ 4)( ϕ $^{4}$/M4 $_{P}$) | , it turns out that M ≥ M$_{P}$ . For a specific parameter space, M ≈ 10 $^{15}$− 10 16 GeV and µ ≈ 10 $^{13}$− 10 14 GeV and n = 2 , 3 , 4 and β ≤ 0 . 03, it is possible to match the amplitude of the perturbations and the spectral tilt within n$_{s}$ = 0 . 96 ± 0 . 014 for N = 60 e-foldings of inflation. The model requires pre-inflationary phase to set the initial conditions for ϕ ≈ 0 to be realizable. Another example of flavon is to consider a vacuum alignment potential as studied in the SU(3) family symmetry model of [85, 709]. It was assumed that < φ$_{23}$ > ∝ (0 , 1 , 1) T and < Σ > = diag( a, a, − 2 a ) are already at their minima, and that the relevant part of the superpotential which governs the final step of family symmetry breaking is given by [709] where a singlet, S , is the driving superfield for the flavon φ$_{123}$ and the non-minimal K¨ ahler potential is given by: During inflation the fields with larger VEVs Y$_{123}$, φ$_{123}$, ¯ φ$_{123}$ do not evolve, the inflationary potential is dominated by 143 W = κS ( ¯ φ$_{123}$φ$_{123}$ − M $^{2}$) + $_{κ}$′$_{Y}$$_{123}$ ¯ φ$_{23}$φ$_{123}$ + $_{κ}$′′$_{Z}$$_{123}$ ¯ φ$_{123}$ Σ φ$_{123}$ + ... . (307) K = | S | 2 + | φ$_{123}$ | 2 + | ¯ φ$_{123}$ | 2 + | Y$_{123}$ | 2 + | ¯ φ$_{23}$ | 2 + | φ$_{23}$ | 2 + | Z$_{123}$ | 2 + | Σ | 2 + κ$_{S}$ | S 4 4 M 2 P + κ$_{SZ}$ S | $^{2}$| Z$_{123}$ 2 4 M 2 P + ... . (308) where | S | = $_{σ/}$√$_{2,}$ | Z$_{123}$ | = $_{ξ/}$√$_{2 and}$ γ = κ$_{SZ}$ − 1. Inflation can happen if the coefficients in front of the mass terms for σ and/or ξ are sufficiently small. The inflaton could be σ if γ < − 1 / 3, the mass of ξ becomes heavy compared to the Hubble scale during inflation. For κ$_{S}$ ≈ (0 . 005 − 0 . 01) and κ ≈ (0 . 001 − 0 . 05), the spectral index is V = κ $^{2}$M4 [ 1 − γ ξ 2 2 M 2 P − 2 κ$_{S}$ σ 2 2 M 2 P + ... ] , (309)