[132, 223]. Present CMB data rules out pure isocurvature perturbation spectrum [13, 224– 231], although a mixture of adiabatic and isocurvature perturbations remains a possibility. In the latter case it has been argued that the adiabatic and isocurvature perturbations might naturally turn out to be correlated [214, 232–234]. It is sometimes useful to consider α defined by: α 1 − α = P S ( k$_{0}$ ) $_{ζ}$( k$_{0}$ ) , (55) where P S ( k$_{0}$ ) is the power spectrum of the entropy perturbation S$_{c}$ at the pivot scale. This parameter α is constrained by observations, see Sec. II E below. 4. Non-Gaussianity The inflaton inevitably has to have interactions with other scalars, fermions and gauge fields for a successful reheating. Furthermore, there could be more than one light scalar dynamics involved during and after inflation. The collective dynamics of more than one light field can source non-Gaussianity [18–22, 235–237] (for a review see [23, 211]). The non-Gaussianity can also be generated by invoking initial conditions which depart from Bunch-Davies vacuum [238], non-canonical kinetic term [239, 240], breaking slow-roll con- ditions abruptly for a brief period [241, 242], multi-field inflationary models [236], curva- ton scenarios [126, 131] and large non-Gaussianity during prehating [243–246]. In [247], non-Gaussianity during preheating has been found less significant when studied in the con- text of δN formalism. The simplest form for the local non-Gaussianity can be written as [156, 183, 213, 248]: ζ ( x ) ≡ g ( x ) + 3 5 f$_{NL}$ g $^{2}$( x ) + 9 25 g$_{NL}$ g $^{3}$( x ) + . . . , (56) where g ( x ) is the Gaussian random fluctuations. In general, the non-Gaussianity can be calculated by studying the bispectrum (three point correlator 〈 g$_{k}$$_{1}$, g$_{k}$$_{2}$, g$_{k}$$_{3}$ 〉 = 0) and the trispectrum (four point correlator 〈 g$_{k}$$_{1}$, g$_{k}$$_{2}$, g$_{k}$$_{3}$, g$_{k}$$_{4}$ 〉 ̸ = 0) $^{11}$. 11 Assuming that ζ is constant and dominated by the Gaussian perturbations, g , the power spec- trum P ζ is determined by, 〈 ζ$_{k}$$_{1}$ ζ$_{k}$$_{2}$ 〉 = (2 π ) $^{3}$P $_{ζ}$( k$_{1}$ ) δ ( k$_{1}$ + k$_{2}$ ), the bispectrum B ζ is deter- mined by 〈 ζ$_{k}$$_{1}$ ζ$_{k}$$_{2}$ ζ$_{k}$$_{3}$ 〉 = (2 π ) $^{3}$B $_{ζ}$( k$_{1}$, k$_{2}$, k$_{3}$ ) δ ( k$_{1}$ + k$_{2}$ + k$_{3}$ ), and the trispectrum T ζ is given by 〈 ζ$_{k}$$_{1}$ ζ$_{k}$$_{2}$ζ$_{k}$$_{3}$ 〉 = (2 π ) $^{3}$B $_{ζ}$( k$_{1}$, k$_{2}$, k$_{3}$ ) δ ( k$_{1}$ + k$_{2}$ + k$_{3}$ ), where B ζ and T ζ can be written as: B $_{ζ}$( k$_{1}$, k$_{2}$, k$_{3}$ ) = (6 / 5) f$_{NL}$ ( P $_{ζ}$( k$_{1}$ ) P ζ ( k$_{2}$ ) + P $_{ζ}$( k$_{2}$ ) P $_{ζ}$( k$_{3}$ ) + P $_{ζ}$( k$_{3}$ ) P $_{ζ}$( k$_{1}$ )), and T $_{ζ}$( k$_{1}$, k$_{2}$, k$_{3}$, k$_{4}$ ) = 24