Primordial Gravitational Waves from Axion-Gauge Fields Dynamics

TL;DR

This work introduces a two-sector inflationary framework where an inflaton drives expansion while a spectator axion–SU(2) gauge field sector, coupled via a Chern-Simons term, sources gravitational waves with a pronounced chirality. By decoupling the spectator dynamics from the inflaton, the model preserves CNI-like tensor phenomenology without conflicting with scalar perturbation bounds, and predicts sizable GW signals even when the vacuum contribution would be subdominant. The tensor signal exhibits chirality and can feature either red or blue tilt, breaking the standard r–V_inf relation and enabling observable GWs at CMB scales for a range of parameters, including lower $H$ and smaller coupling $λ$. The study also analyzes backreaction, identifies viable regions of parameter space, and discusses extensions to lower inflation scales, reheating aspects, and potential non-Gaussian signatures. This framework broadens the landscape of inflationary GW production with distinct observational signatures and practical implications for upcoming experiments.

Abstract

Inspired by the chromo-natural inflation model of Adshead&Wyman, we reshape its scalar content to relax the tension with current observational bounds. Besides an inflaton, the setup includes a spectator sector in which an axion and SU(2) gauge fields are coupled via a Chern-Simons-type term. The result is a viable theory endowed with an alternative production mechanism for gravitational waves during inflation. The gravitational wave signal sourced by the spectator fields can be much larger than the contribution from standard vacuum fluctuations, it is distinguishable from the latter on the basis of its chirality and, depending on the theory parameters values, also its tilt. This production process breaks the well-known relation between the tensor-to-scalar ratio and the energy scale of inflation. As a result, even if the Hubble rate is itself too small for the vacuum to generate a tensor amplitude detectable by upcoming experiments, this model still supports observable gravitational waves.

Figures (8)

• Figure 1: (Left panel) The background evolution of the axion $\chi(t)/f$ (blue) and the gauge field $10^{-2}\Lambda=5Q(t)/f$ (yellow) are shown. The slow-roll expression $Q_{\min}(\chi)$, into which the numerically obtained $\chi(t)$ and $H(t)$ are plugged, is also plotted (green dashed line) and it coincides with the numerical one. (Right panel) The energy density of the inflaton $\rho_\phi$ (blue), the axion $\rho_\chi$ (yellow), the gauge field $\rho_B\equiv 3g^{2}Q^4/2$ (green), $\rho_E \equiv 3(\dot{Q}+HQ)^2/2$ (red) and the tensor fluctuation $\rho_{t_R}$ defined in eq. \ref{['rho tR']} (purple dashed) are shown. The inflaton always dominates the total energy density of the universe during inflation.
• Figure 2: (Left panel) The contributions to $\epsilon_H$ from the various components are shown, $\epsilon_H =\epsilon_{\phi}+\epsilon_{\chi}+\epsilon_{B}+\epsilon_{E}$. $\epsilon_\phi$ dominates $\epsilon_H$ and determines the evolution of $H$. (Right panel)$m_Q\equiv g Q/H$ is plotted. The shape of the resultant power spectrum of GW is basically determined by the time evolution of $m_Q$ as shown in §\ref{['sec:tensors']}.
• Figure 3: (Left panel)$\mathcal{F}^2(m_Q)$ defined below \ref{['PQh']} is evaluated under the slow-roll approximation. It is roughly approximated by $\exp(3.6m_Q)$ (yellow dashed line). (Right panel) The constraint on $m_Q$ and $\epsilon_B$ for $g=10^{-2}$ based on the analytic estimation of the sourced GW. In the blue shaded region, the sourced GW is smaller than one from the vacuum fluctuation ($R_{\rm GW}<1$). In the upper shaded region, the observational upper bound on the tensor-to-scalar ratio ($r<0.07$) is violated. The green and purple dashed lines denote $r_{\rm vac}=10^{-3}$ and $r=10^{-3}$, respectively. In the red shaded region, the backreaction on the EoM for $Q$ and $\chi$ is significant as discussed in §\ref{['sec:backreaction']}.
• Figure 4: (Left panel) The mode functions of the tensor fluctuation with the right helicity, $\psi_R(x)$ and $t_R(x)$, normalized by $\sqrt{2k}x$ for $k=k_*$. $t_R$ reaches its peak and sources $\psi_R$ slightly before horizon crossing ($x=1$; vertical dotted line). After horizon crossing, $\psi_R$ remains constant. (Right panel) The resultant $\mathcal{P}_h$ (blue), $\mathcal{P}_h$ contributed only by the vacuum fluctuation (red) and $\mathcal{P}_h$ estimated by the analytic expression (yellow dashed) are shown. The green and purple lines denote $r=10^{-3}$ and $0.07$, respectively. $\mathcal{P}_h$ is substantially enhanced by the axion-gauge spectator sector.
• Figure 5: (Left panel) The numerically obtained scalar perturbations in the axion-gauge sector, $\Delta_i\ (i=1,2,3)$. The axion fluctuation $\Delta_1$ freezes after horizon crossing, while its amplitude is much smaller than in the standard massless case, $\sqrt{2k}x \Delta=1$. The scalar modes of the gauge field, $\Delta_2$ and $\Delta_3$, evolve on super-horizon scales depending on the axion mass $U_{\chi\chi}$, but their amplitudes are negligible. (Right panel) The spectrum of $x\Delta_1$ in the super-horizon limit. The amplitude is $\mathcal{O}(10^{-1})$ and $\delta\chi$ induces only negligible $\delta\phi$.