where V$_{σσ}$ ≪ H 2 during inflation, therefore the VEV is σ ≈ $^{σ}$∗ nearly a constant. The perturbations in σ field is given by: δσ/σ ∼ ( H$_{inf}$ / 2 $^{πσ}$∗ ) for H$_{inf}$ ≪ $^{σ}$∗ , therefore P 1 / 2 δσ/σ ∼ ( H$_{inf}$/ 2 $^{πσ}$∗ ). It is assumed that the curvaton field rolls slowly as the universe becomes radiation dominated after the inflaton decay. On large scales the curvature perturbations are given by: ζ = − Hδt = − Hδρ/ ˙ ρ , ζ$_{r}$ = (1 / 4) δρ$_{r}$/ρ$_{r}$ and ζ$_{σ}$ = (1 / 3) δρ$_{σ}$/ρ$_{σ}$ ≡ (1 / 3) δ$_{σ}$ , they all evolve independently [251]. The value of ζ$_{σ}$ has been calculated assuming that the curvaton is oscillating with a pressureless equation of state. During these oscillations the curvaton converts its fluctuations into the curvature perturbations. The total curvature perturbations is given by [126, 131]: Since prior to the curvaton oscillations, the curvature perturbations in the universe is domi- nated by that of the inflaton decay products, i.e. radiation, therefore, ζ = ζ$_{r}$ , which simplifies the above expression: If the curvaton energy density dominates over radiation, then ζ = (1 / 3) δ$_{σ}$ , otherwise, the fraction, r ∼ ρ$_{σ}$/ρ$_{r}$ < 1, would signify the curvaton energy density at the time of decay. In which case ζ = (1 / 4) rδ$_{σ}$ , and Since ˙ H$_{inf}$ /H 2 $_{inf}$, V$_{σσ}$/H 2 inf ≪ 1, the spectral tilt is fairly close to one. The coherent oscillations of the curvaton generates non-Gaussian perturbations. A small perturbations around the minimum leads to averaged over many-many oscillations over Hubble period. In some realistic curvaton sce- narios, the curvaton may decay almost instantly via SM gauge couplings in less than one Hubble time scale. In which case the curvaton oscillations may not last long enough to generate any significant non-Gaussianity. 26 and the spectral tilt is given by ζ = 4 ρ$_{r}$ζ$_{r}$ + 3 ρ$_{σ}$ζ$_{σ}$ 4 ρ$_{r}$ + 3 ρ$_{σ}$ . (61) ζ = ρ$_{σ}$ 4 ρ$_{r}$ + 3 ρ$_{σ}$ δ$_{σ}$ . (62) P ζ ≈ r 2 ( H$_{inf}$ 2 $^{πσ}$∗ ) 2 , (63) n$_{s}$ ≡ 1 − 6 ϵ + 2 η = 1 + ˙ H$_{inf}$ H 2 inf + 2 3 V$_{σσ}$ H 2 inf . (64) δρ$_{σ}$ ρ$_{σ}$ = 2 δσ σ + ( δσ ) 2 σ 2 , (65)