Full Parity-Violating Trispectrum in Axion Inflation: Reduction to Low-D Integrals

TL;DR

This paper develops a method to simplify the complex calculations of the primordial trispectrum in axion inflation models with parity violation, enabling future observational constraints from galaxy surveys.

Contribution

It introduces a novel analytical reduction technique for high-dimensional trispectrum integrals in axion inflation models with parity violation.

Findings

Analytical reduction of high-dimensional integrals to low-dimensional radial integrals.

Efficient numerical evaluation of the primordial trispectrum.

Framework for constraining parity-violating inflationary models with galaxy survey data.

Abstract

Recent measurements of the galaxy 4-Point Correlation Function (4PCF) have seemingly detected non-zero parity-odd modes at high significance. Since gravity, the primary driver of galaxy formation and evolution is parity-even, any parity violation, if genuine, is likely to have been produced by some new parity-violating mechanism in the early Universe. Here we investigate an inflationary model with a Chern-Simons interaction between an axion and a $U(1)$ gauge field, where the axion itself is the inflaton field. Evaluating the trispectrum (Fourier-space analog of the 4PCF) of the primordial curvature perturbations is an involved calculation with very high-dimensional loop integrals. We demonstrate how to simplify these integrals and perform all angular integrations analytically by reducing the integrals to convolutions and exploiting the Convolution Theorem. This leaves us with low-dimensional radial integrals that are much more amenable to efficient numerical evaluation. This paper is the first in a series in which we will use these results to compute the full late-time 4PCF for axion inflation, thence enabling constraints from upcoming 3D spectroscopic surveys such as Dark Energy Spectroscopic Instrument (DESI), Euclid, or Roman.