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