content_image/351841.jpg content_image/351845.jpg
[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: 

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 

<img src='content_image/351841.jpg'>

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]: 

<img src='content_image/351845.jpg'>

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) $^{11}$. 

