Axion-Sourced Gravitational Waves in $\mathrm{B}-\mathrm{L}$ Hybrid Inflation

Abstract

Minimal supersymmetric $\mathrm{B}-\mathrm{L}$ hybrid inflation predicts a negligible vacuum tensor-to-scalar ratio $r_{\mathrm{vac}}\sim 10^{-8}$ due to its extremely flat potential. In this letter, we show that adding a spectator pseudoscalar axion-like field coupled to the $\mathrm{U}(1{)}_{\mathrm{B}-\mathrm{L}}$ gauge sector via a Chern-Simons term circumvents this suppression. The rolling axion triggers a tachyonic instability for one gauge field helicity, exponentially amplifying gauge fluctuations. These sourced modes generate a stochastic gravitational-wave background with tensor power spectrum ${\mathcal{P}}_T^{\mathrm{src}}\propto e^{4\pi \xi }/{\xi }^6$, where $\xi =\alpha \dot{\varphi }/(2f_{a}H)$ is the gauge-field instability parameter. For $\xi \sim 3.3$--$3.6$, the tensor-to-scalar ratio reaches $r\sim 10^{-3}$, within the sensitivity of LiteBIRD. For $\xi \sim 3.6$, the gravitational-wave spectrum develops a peaked shape that enters the LISA sensitivity band (peaking at frequencies around $10^{-3}$ Hz) with an amplitude $h^2{\Omega }_{\mathrm{GW}}\sim 2.5\times 10^{-13}$. The mechanism predicts chiral gravitational waves, a broken consistency relation $r=16ϵ$, and a distinctive $r$--${\Omega }_{\mathrm{GW}}$ correlation that could be tested by future CMB and interferometer observations.

Comments: 5 pages, 2 figures, to be submitted to PRL