Statistics of general functions of a Gaussian field -application to non-Gaussianity from preheating-

Understand

We provide a general formula for calculating correlators of arbitrary function of a Gaussian field.

• This work extends the standard leading-order approximation based on the delta N formalism to the case where truncation of the delta N at some low order does not yield the correct answer.
• As an application of this formula, we investigate 2, 3 and 4-point functions of the primordial curvature perturbation generated in the massless preheating model by approximating the mapping between the curvature perturbation and the Gaussian field as a sum of the many spiky normal distribution functions as suggested by lattice calculations.
• We also discuss observational consequences of this case and show that trispectrum would be a key observable to search signature of preheating in the CMB map.