content_image/312987.jpg content_image/312988.jpg content_image/312989.jpg
Therefore the δN formalism to third order gives 

<img src='content_image/312987.jpg'>

By substituting our mass definition and its differential, Eqs. (4.3) and (4.4), into Eq. (4.63) we obtain the power spectrum of the primordial curvature perturbation, which to first order is 

<img src='content_image/312988.jpg'>

The condition for the perturbative expansion in Eq. (4.63) to be suitable, i.e. that each term is much smaller than the preceding one, yields the same constraint as in Eq. (4.61). 

## 4.4.2 Non-Gaussianity 

One of the distinct observational signatures that we hope to generate through this model is the production of characteristic and observable non-Gaussianity in the curvature perturbation. Non-Gaussianity refers to the departure that the distribution of, in this particular case, the curvature perturbation is from purely Gaussian, i.e. of the familiar bell-shaped distribution. For a purely Gaussian distribution, there is no correlation between different modes of the perturbation. For a non-Gaussian distribution however, there is correlation, with the 3-point correlator for the curvature perturbation being [1] 

<img src='content_image/312989.jpg'>

