Suppression of scalar perturbations due to a heavy axion

TL;DR

The authors address the challenge of generating observable gravitational waves during inflation without overproducing scalar perturbations. They introduce a two-field setup with a heavy axion $m_{\rm \chi} \gg H$ dragged by a light inflaton along a curved valley $U(\phi,\chi)$, which triggers a brief tachyonic production of gauge quanta and sources both scalar and tensor modes. By ensuring $m_{\chi}^{2} \gg H^{2}$, the dominant scalar sourcing from $\delta\chi$ is suppressed, while tensor perturbations sourced by the gauge fields are preserved and amplified, yielding a sizable $r$ (e.g., $r \approx 0.026$) compatible with current bounds and potentially detectable by future CMB experiments. The concrete Starobinsky-like model demonstrates that $\,\mathcal{P}_{\mathcal{R}}^{\mathrm{s}}$ remains much smaller than the vacuum ${\cal P}_{\mathcal{R}}^{\mathrm{v}}$, while the GW energy density is enhanced, offering a viable observational window into axion–gauge dynamics during inflation.

Abstract

A fast-rolling axion can transfer its kinetic energy to gauge fields via the Chern-Simons coupling, leading to copious production of gauge quanta during inflation. The amplified gauge fields act as a source for both scalar and tensor perturbations. In this work, we propose a mechanism for suppressing scalar perturbations while sourcing strong tensor perturbations. We present an implementation of such a mechanism, demonstrating that sourced tensor perturbations are expected to be detected by upcoming next-generation CMB experiments.

Figures (6)

• Figure 1: Schematic illustration of the coupling $U(\phi,\chi)$. The color denotes the value of $U(\phi,\chi)$, varying from red at low values to green at high values. The black dashed trajectory superimposed on the surface traces the partial-minimum valley, defined by the condition $\partial_{\chi} U(\phi,\chi) = 0$.
• Figure 2: Landscape of the coupling \ref{['eq: U_g']}. The light blue trajectory represents the solution of Eq. \ref{['eq: phi_eom_realize']} and Eq. \ref{['eq: chi_eom_realize']}. This trajectory includes a rapid turn as it nearly reaches the $\phi$-axis, at which point gauge quanta are exponentially produced due to the tachyonic instability.
• Figure 3: Evolution of $\xi$ as a function of $N$. In the region where $\xi \gg 1$, the axion field $\chi$ enters a fast-roll phase, leading to the exponential production of gauge quanta.
• Figure 4: Evolution of the coupling term $m_{\chi}^{2} (\chi - g(\phi)) g_{,\phi}(\phi)$ in Eq. \ref{['eq: phi_eom_realize']} and the mass ratio $m_{\phi}^2/m_{\chi}^2$.
• Figure 5: Sourced scalar power spectrum $\mathcal{P}_{\mathcal{R}}^{\mathrm{s}}(\tau_{\mathrm{end}}, k)$ on CMB scales. It is computed numerically using Eq. \ref{['eq: PR']}. The induced peak amplitude is approximately $10^{-4}$ times smaller than the amplitude of vacuum power spectrum, $\mathcal{P}_{\mathcal{R}}^{\mathrm{v}} \approx 2.1 \times 10^{-9}$, on CMB scales.