where the origin of V$_{0}$ arises from the Peccei-Quinn breaking scale, Λ = 2 πf$_{a}$ , where 10 10 ≤ f ≤ 10 13 GeV. The phase transition associated with the spontaneous breaking of family symmetry, by flavons, which is responsible for the generation of the effective quark and lepton Yukawa couplings could also be responsible for inflation [85]. In order to understand the origin of fermion masses and mixing, one can extend the SM by some horizontal family symmetry G$_{F}$ , which may be continuous or discrete, and gauged or global. It must be broken at high scales with the help of flavons, φ , whose VEV will break the family symmetry. The Yukawa couplings are generically forbidden by the family symmetry G$_{F}$ , but once it is broken, effective Yukawa couplings can be generated by non- renormalizable operators, i.e. ( φ/M$_{c}$ ) $^{n}$ψψ$^{c}$H . This gives rise to an effective Yukawa coupling ε $^{n}$ψψ$^{c}$H , where ε = 〈 φ 〉 /M$_{c}$ ∼ O (0 . 1) and ψ, ψ c are SM fermion fields, H is a SM Higgs field, and M$_{c}$ is the messenger scale. The relevant superpotential for inflation can be given by [85, 707]: for n ≥ 1 and κ ∼ 1. The fields, φ = ( φ$_{1}$, φ$_{2}$, φ$_{3}$ ) is in the fundamental triplet 3 representation of A$_{4}$ or Δ$_{27}$. At the global minimum of the potential, the φ$_{i}$ components get VEVs of order M = $^{M}$∗ ( µ M$_{∗}$ ) 2 / 3 n $^{73}$. The K¨ ahler potential is of the non-minimal form [85, 707] W = κS [ ( φ$_{1}$φ$_{2}$φ$_{3}$ ) n M 3 n − 2 ∗ − µ 2 ] (304) K = | S | 2 + | φ | 2 + κ$_{2}$ | S | $^{2}$| φ | 2 M 2 P + κ$_{1}$ | φ | 4 4 M 2 Pl + κ$_{3}$ | S | 4 4 M 2 Pl + ... (305) 73 The initial motivations were proposed in [337, 707] in order to obtain a phenomenologically viable new inflationary potential from the superpotential: W = S ( − µ 2 + ( ¯ ΦΦ) $^{m}$/M 2 m − 2 ∗ ). Here ¯ Φ(Φ) denotes a conjugate pair of superfields charged under some gauge group, and S is a gauge singlet. There is an U (1)$_{R}$ symmetry under which Φ → Φ, ¯ Φ → ¯ Φ, S → e i 2 $^{α}$S and W → e i 2 $^{α}$W . Under these symmetries m = n for odd n and m = n/ 2 otherwise. Along the D -flat direction, the k¨ ahler potential is given by; K = | S | $^{2}$+ (2 | Φ | $^{2}$+ κ$_{1}$ | Φ | $^{4}$/ 4 M 2 $_{P}$+ κ$_{2}$ | S | $^{2}$| Φ | $^{2}$/M2 $_{P}$)+ κ$_{3}$ | S | $^{4}$/ 4 M 4 $_{P}$. . . . The resultant potential is given by: V ≈ µ $^{4}$(1 − κ$_{3}$ S $^{2}$/M2 $_{P}$+2(1 − κ$_{2}$ ) | φ | $^{2}$/M2 P − 2 | φ | 2 $^{m}$/M 2 m ∗ + . . . ). For κ$_{3}$ < − 1 / 3, the S field obtains heavy mass compared to the Hubble expansion rate and the field rolls to its minimum in one e-foldings leaving behind the dynamics of φ field to slowly roll over the potential; V ≈ µ $^{4}$(1 − 0 . 5( κ$_{2}$ − 1) φ $^{2}$/M2 P − 2 φ 2 $^{m}$) [708]. The spectral can match the CMB data for values of m = 2 − 5 with a negligible running of the spectral index dn$_{s}$/d ln k ≤ 10 − $^{3}$. One particular issue is that the initial condition for φ field which needs close to zero VEV, this is a nontrivial initial condition, one proposal is to have a pre-inflationary phase. 142