representation of a gauge group have the same parameter A $_{i}$. This implies that [122] Σ$_{tot}$ ≡ 3 ∑ i,j =1 2 ∑ a,b =1 3 ∑ α,β $_{=1}$A i,a,α A j,b,β 〈 σ$_{tot}$v$_{rel}$ 〉 = 1 32 M 2 P ∑ [6 α$_{3}$ (2 A 2 Q + A 2 u + A 2 $_{d}$) + 9 4 α$_{2}$ (3 A 2 Q + A 2 L + A 2 $_{H}$) + 1 4 α$_{1}$ ( A 2 Q + 8 A 2 u + 2 A 2 d + 3 A 2 L + 6 A 2 e + 3 A 2 $_{H}$)] , (440) where 1 ≤ i, j ≤ 3, a, b = 1 , 2 and 1 ≤ α, β ≤ 3 are the flavor, weak-isospin and color indices of scattering degrees of freedom respectively. Also α$_{3}$ , α$_{2}$ and α$_{1}$ are the gauge fine structure constants related to the SU (3)$_{C}$, SU (2)$_{W}$ and U (1)$_{Y}$ groups respectively. The sum is taken over the three flavors of Q, u, d, L, e and the two Higgs doublets. After replacing Σ$_{tot}$ in Eq. (439), and recalling that T$_{max}$ ≈ m$_{φ}$/ 3, we obtain [122] n$_{3}$$_{/}$$_{2}$ s ≃ ( $_{10}$− $^{1}$M2 P Σ$_{tot}$ ) ( 228 . 75 A ) 5 / 4 ( T$_{max}$ 10 10 GeV ) $_{10}$− $^{12}$. (441) 2 Note that in full thermal equilibrium, Σ$_{tot}$ = (4 π/M 2 $_{P}$) × (16 α$_{3}$ + 6 α$_{2}$ + 2 α$_{1}$ ) ≃ (10 − $^{1}$/M2 $_{P}$) (up to logarithmic corrections which are due to renormalization group evolution of gauge couplings). Let us consider a simplistic scenario when the inflaton primarily decays into one fla- vor of LH (s)quarks. In this case A Q = 1 / 24 for the relevant flavor $^{103}$, while A = 0 for the rest of the degrees of freedom. This results in a gravitino abundance: n$_{3}$$_{/}$$_{2}$/s ≃ ( A / 228 . 75) 3 / 4 ( T$_{max}$/ 10 10 GeV) 10 − $^{12}$, where A is given by Eq. (435) and note that T$_{max}$ ≫ T$_{R}$ . The largest value for T$_{max}$ ≃ 10 12 GeV, therefore the the tightest bound for unstable gravitinos come from BBN ( n$_{3}$$_{/}$$_{2}$/s ) ≤ 10 − 16 (arising for m$_{3}$$_{/}$$_{2}$ ≃ 1 TeV and a hadronic branching ratio ≃ 1) is satisfied if A ≤ 10 − $^{6}$. Much weaker bounds on A are found for a radiative decay. For example, A ≤ 10 − 3 (1) if m$_{3}$$_{/}$$_{2}$ ≃ 100 GeV (1 TeV). The curvaton scenario is an interesting possibility [126, 127, 129–132, 822], see also [128], where the perturbations of more than one light scalar fields play important role during VII. GENERATING PERTURBATIONS WITH THE CURVATON A. What is the curvaton ? 103 The total number of degrees of freedom in one flavor of LH (s)quarks is 2 (particle − antiparticle) × 2 (fermion − boson) × 2 (weak − isospin) × 3 (color). 206