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

TL;DR

This paper derives a general formula for correlators of functions of Gaussian fields, extending the delta N formalism, and applies it to analyze non-Gaussianity from preheating, highlighting the trispectrum as a key observational signature.

Contribution

It introduces a comprehensive formula for correlators of arbitrary functions of Gaussian fields, improving upon the delta N formalism for non-Gaussianity calculations in preheating models.

Findings

The curvature correlation functions match local type forms at leading order.

The standard non-linearity parameters formula remains valid with a smoothed e-folding number.

The trispectrum is identified as a crucial observable for preheating signatures.

Abstract

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. It is found the forms of the curvature correlation functions for any delta N, at the leading order in the correlator of the Gaussian field, coincide with the standard local type ones. Within this approximation, it is also found that the standard formula for the non-linearity parameters given by the product of the derivatives of the e-folding number still holds after we replace the bare e-folding number appearing in the original delta N expansion with the one smoothed in the field space with a Gaussian window function.