Parity-Odd and Even Trispectrum from Axion Inflation

TL;DR

This paper investigates the parity-odd and even components of the four-point correlation function in axion inflation models, revealing that parity-odd signals are smaller but potentially detectable, with implications for understanding early universe physics.

Contribution

It provides a detailed analysis of parity-odd and even trispectra in axion inflation, including numerical evaluation of their magnitudes for different vector field masses.

Findings

Parity-even signals are significant for both massive and massless vector fields.

Parity-odd signals are about one to two orders of magnitude smaller.

Numerical methods are developed to evaluate the correlation functions efficiently.

Abstract

The four-point correlation function of primordial scalar perturbations has parity-even and parity-odd contributions and the parity-odd signal in cosmological observations is opening a novel window to look for new physics in the inflationary epoch. We study the distinct parity-odd and even prediction from the axion inflation model, in which the inflaton couples to a vector field via a Chern-Simons interaction, and the vector field is considered to be either approximately massless ($m_A \ll $ Hubble scale $H$) or very massive ($m_A \sim H $). The parity-odd signal arises due to one transverse mode of the vector field being predominantly produced during inflation. We adopt the in-in formalism to evaluate the correlation functions. Considering the vector field mode function to be dominated by its real part up to a constant phase, we simplify the formulas for numerical computations. The numerical studies show that the massive and massless vector fields give significant parity-even signals, while the parity-odd contribution is about one to two orders of magnitude smaller.