Four-point correlation functions in axion inflation

TL;DR

This paper investigates parity violation during axion inflation by calculating four-point correlation functions, revealing parity-odd components that align with recent galaxy survey observations.

Contribution

It introduces a novel calculation of four-point functions in axion inflation using an open quantum system approach, highlighting parity-odd effects in the correlation coefficients.

Findings

Identification of parity-odd components in four-point functions.

Derivation of the lowest-order nonvanishing parity-odd coefficient $A6_{234}$.

Consistency of derived coefficients with recent galaxy survey data.

Abstract

We study parity violation in the early universe by examining the four-point correlation function within the axion inflation model. Using an open quantum system formalism from our previous work, we calculate the influence functional to fourth order, from which we then derive the inflaton four-point correlation function. When we decompose this function using isotropic basis functions, the expansion coefficients $\zeta_{\ell',\ell'',\ell'''}$ naturally split into parity-even and parity-odd components. In the large $\xi$ approximation, which enhances the production of right-handed photons in the model, the derivation of these coefficients simplifies. We work out the lowest-order nonvanishing parity-odd $\zeta_{234}$ term which clearly indicates the presence of parity violation. Moreover, our derived values of the coefficients are consistent with recent observational data from galaxy surveys.