Axion Inflation with an SU(2) Gauge Field: Detectable Chiral Gravity Waves

TL;DR

This paper explores an axion inflation model with an SU(2) gauge field that produces detectable chiral gravitational waves without conflicting with current scalar fluctuation observations.

Contribution

It demonstrates that gauge field fluctuations can generate observable chiral gravitational waves while minimally affecting scalar perturbations, in a model-independent inflation framework.

Findings

Chiral gravitational waves are linearly coupled to gravitational waves.

Gauge field fluctuations produce a circularly polarized tensor spectrum.

Scalar fluctuations remain consistent with current CMB observations.

Abstract

We study a single field axion inflation model in the presence of an SU(2) gauge field with a small vev. In order to make the analysis as model-independent as possible, we consider an arbitrary potential for the axion that is able to support the slow-roll inflation. The gauge field is coupled to the axion with a Chern-Simons interaction $\frac{\lambda}{f}F_{\mu\nu}^a\tilde F_a^{\mu\nu}$ where $\frac{\lambda}{f}\sim\mathcal{O}(10)$. It has a negligible effect on the background evolution, $\frac{\rho_{_{\rm YM}}}{M_{\rm Pl}^2H^2}\lesssim\epsilon^2$. However, its quantum fluctuations make a significant contribution to the cosmic perturbation. In particular, the gauge field has a spin-2 fluctuation which explicitly breaks the parity between the left- and right-handed polarization states. The chiral tensor modes are linearly coupled to the gravitational waves and lead to a circularly polarized tensor power spectrum comparable to the unpolarized vacuum power spectrum. Moreover, the scalar sector is modified by the linear scalar fluctuations of the gauge field. Since the spin-0 and spin-2 fluctuations of the SU(2) gauge field are independent, the gauge field can, at the same time, generate a detectable chiral gravitational wave signal and have a negligible contribution to the scalar fluctuations, in agreement with the current CMB observations.