Tensor Adiabatic Modes and Consistency Relations with Primordial Axion-Gauge Fields

TL;DR

This paper investigates tensor modes in axion inflation models with SU(2) gauge fields, revealing that gravity waves are adiabatic and exhibit chiral imprints, which could serve as observational signatures of such gauge fields during inflation.

Contribution

It demonstrates that tensor perturbations in axion-SU(2) inflation models obey Maldacena's consistency relation and identifies chiral signatures in n-point functions as observable imprints.

Findings

Gravity waves are adiabatic in this setup.

Chiral n-point functions depend on gauge field density.

Consistency relation holds despite gauge field contributions.

Abstract

We study the tensor consistency relation in models of axion inflation with an SU(2) gauge field. In the tensor sector, we have two spin-2 modes, the standard gravity waves and the tensor perturbations of the SU(2) gauge field which sources the gravity waves at the linear level. Interestingly enough, we find that the gravity waves are adiabatic and Maldacena's consistency relation including a long wavelength gravity wave holds in this setup. However, since it is partially polarized, there is a difference between the (n+1)-point functions with different helicity states proportional to the ratio of the gauge field density to the total density. These chiral n-point functions are the imprints of the SU(2) gauge field on the primordial cosmological perturbations and a robust observational feature of their contribution to the physics of inflation.