Mode coupling evolution in arbitrary inflationary backgrounds

TL;DR

This paper analyzes the evolution of high-order correlation functions of a test scalar field during arbitrary inflationary backgrounds, providing explicit formulas and comparing different inflation models to understand non-Gaussian features.

Contribution

It extends previous results by deriving exact expressions for correlation functions in general inflationary backgrounds, including power law and chaotic inflation, using quantum-to-classical mapping.

Findings

High-order correlations are amplified by nearly an order of magnitude in non-de Sitter backgrounds.

Late-time bispectrum and trispectrum amplitudes are expressed in terms of expansion factor behavior.

Non-Gaussian parameters like f_NL depend on wave-modes at the percent level.

Abstract

The evolution of high order correlation functions of a test scalar field in arbitrary inflationary backgrounds is computed. Whenever possible, exact results are derived from quantum field theory calculations. Taking advantage of the fact that such calculations can be mapped, for super-horizon scales, into those of a classical system, we express the expected correlation functions in terms of classical quantities, power spectra, Green functions, that can be easily computed in the long-wavelength limit. Explicit results are presented that extend those already known for a de Sitter background. In particular the expressions of the late time amplitude of bispectrum and trispectrum, as well as the whole high-order correlation structure, are given in terms of the expansion factor behavior. When compared to the case of a de Sitter background, power law inflation and chaotic inflation induced by a massive field are found to induce high order correlation functions the amplitudes of which are amplified by almost one order of magnitude. These results indicate that the dependence of the related non-Gaussian parameters - such as f_NL - on the wave-modes is at percent level.