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

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.

32 pages, 8 figures, one subsection and a few references added, version accepted for publication in JCAP

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Cited by in corpus (11)

• On the Anisotropy of the Gravitational Wave Background from Massless Preheating
• A Cosmic Microscope for the Preheating Era
• Parametric Resonance of Entropy Perturbations in Massless Preheating
• Non-Gaussian CMB and LSS statistics beyond polyspectra
• The primordial curvature perturbation from lattice simulations
• Non-perturbative $\delta N$
• High-redshift Mini-haloes from Modulated Preheating
• Cosmological Signatures of Neutrino Seesaw Mechanism
• Deriving super-horizon curvature perturbations from the dynamics of preheating
• Cosmological Non-Gaussianity from Neutrino Seesaw Mechanism
• Curvature perturbations from preheating with scale dependence