Supercooled Audible Axions

TL;DR

The paper investigates supercooled audible axions, where delaying the onset of ALP oscillations expands the viable parameter space for generating a stochastic gravitational-wave background through tachyonic amplification of gauge fields. By introducing a supercooling ratio $r_{\mathrm{sc}}$, the authors show that a lower Hubble rate at oscillation enhances the ALP energy density at onset and reduces the required coupling to the gauge field, enabling observable GWs for $\alpha$ near unity and $f_\phi$ well below the Planck scale. They analyze two scenarios: ALP–dark photon and ALP–Standard Model photon, deriving cosmological constraints (including $N_{\mathrm{eff}}$ bounds and DM overproduction) and predicting GW spectra with a fit template, highlighting that delayed oscillations shift the peak amplitude and frequency. The SM-photon case introduces finite-temperature dispersion and Schwinger pair production, restricting but not excluding observable regions, with promising signals in the $\mu$Hz to ultra-high-frequency bands, depending on the reheating history and the suppression of the axion relic abundance. Overall, the work broadens the testable landscape for axion-like particles via gravitational waves and motivates further lattice studies and model-building to refine the relic-density constraints and backreaction dynamics.

Abstract

In the audible axion mechanism, axion-like particles source primordial gravitational waves via their coupling to a dark Abelian gauge field. The original setup, however, relies on a large axion decay constant and coupling to produce sizable signals. In this article, we show that delaying the onset of axion oscillations opens up the testable parameter space and reduces the required coupling to $α\gtrsim 1$. Furthermore, we investigate the emission of gravitational waves via the axion coupling to the Standard Model photon in the presence of Schwinger pair production, generating a strong signal in the $μ$Hz or ultra-high frequency range. Cosmological constraints and gravitational wave projections are provided for both scenarios.

Figures (10)

• Figure 1: Overview of the available parameter space for supercooled ALP-dark photon systems, imposing $\alpha=50$ (left) and $\alpha=2\alpha_{\hbox{\scriptsize min}}$ (right), respectively. In both panels, we set $\theta=1$. The dotted lines indicate cosmologically stable ALPs, while the dash-dotted lines signal axion decays before BBN. In the white-shaded region, dark photons violate bounds on the effective number of degrees of freedom at BBN, even in the case without supercooling. The solid lines show the parameter spaces consistent with axion dark matter (eq. \ref{['eq:eps_sup_DM']}) and $N_\mathrm{eff}$ (eq. \ref{['eq:eps_sup_Neff']}) constraints for a suppression of the axion abundance $\epsilon_{\hbox{\scriptsize sup}} \in \{10^{-2},10^{-4},10^{-6}\}$. The color contours display the GW peak amplitude \ref{['eq:GW_peak_estimates_today']}, which is significantly enhanced when decreasing $\alpha$.
• Figure 2: Observational prospects of future GW observatories for ALPs coupled to dark photons, installing $\theta=1$ (both), $\alpha=50$ (left), and $\alpha = 2\alpha_{\hbox{\scriptsize min}}$ (right). The colored solid lines correspond to delayed ALP oscillations, while the dashed lines indicate the original setup without supercooling. Again, the dotted (dash-dotted) lines show the parameter space where the ALP is stable until today (BBN). Constraints from black hole (BH) superradiance AxionLimitsBaryakhtar:2020gaoStott:2020gjjHoof:2024qukUnal:2020jiyWitte:2024drgCardoso:2018tly are displayed by the gray-shaded regions. Delayed oscillations significantly enhance the peak amplitude, extending the observable parameter range by up to two orders of magnitude in $f_\phi$. In addition, supercooled oscillations allow for a smaller ALP-dark photon coupling $\alpha$, further improving detection prospects. Note, however, that most of the parameter space requires a large suppression of the ALP abundance through the tachyonic instability to avoid overclosure.
• Figure 3: Frequencies in the tachyonic production band for the dark photon with zero-temperature dispersion relation (dark blue, top), SM photon without supercooling with full dispersion relation (red dots), and approximated dispersion relation (first order in $\omega$) without (yellow) as well as with sufficient supercooling (light blue). Also included are the peak positions for zero- and finite-$T$ as well as the $k^3$-scaling of the peak (gray dashed). The presented example is for $m_\phi=10^{8}\,\mathrm{GeV}$, $f_\phi=10^{18}\,\mathrm{GeV}$. The original finite-$T$ curve is multiple orders below the ALP mass (black horizontal). Once we impose supercooling with $r_{\hbox{\scriptsize sc}}=2.5 \times 10^{-8}$, the curve is lifted, surpassing the ALP mass and thus opening the tachyonic band.
• Figure 4: Maximum photon energy density for $\alpha=2\alpha_{\hbox{\scriptsize min}}$ and $\theta=1$ in the presence of Schwinger pair production. The colored curves correspond to different choices of $f_\phi$, while the reheating temperature is determined by the axion mass. In the small- (large-)$m_\phi$ regime, the Schwinger effect is suppressed by the vacuum (thermal) mass of the electron.
• Figure 5: Projected positions of the GW peak in the ALP-SM photon scenario. The colored curves indicate the sensitivity regions of the future observatories SKA, $\mu$ARES, LISA, BBO, and ET. We identify two distinct parameter regions where Schwinger pair production is suppressed, allowing for a sizable GW signal. In the low-frequency (small-$m_\phi$) regime, the color coding indicates the required suppression of the abundance for the ALP to constitute DM. In the high-frequency (large-$m_\phi$) regime, ALPs decay before BBN, hence evade all cosmological bounds. ALPs undergoing the tachyonic resonance close to BBN show the most promising observational prospects. Since the characteristic scale of the fluctuations is deep inside the Hubble horizon, the corresponding GW peak lies in the sensitivity region of $\mu$ARES.