Parametric-Resonance Production of QCD Axions

Abstract

We demonstrate that dark matter axion production is enhanced through a natural and unavoidable mechanism: primordial temperature fluctuations periodically modulate the axion mass during the QCD phase transition, thereby triggering parametric resonance in axion field evolution. This interplay between parametric resonance and the misalignment mechanism shifts the predicted axion mass window for the observed dark matter abundance to $10^{-4}-10^{-3} \, \text{eV}$, displacing the canonical axion mass window to previously unexplored higher ranges.

Figures (3)

• Figure 1: Mathieu instability chart showing the largest Floquet exponent $\mathrm{Re}(\mu)$ in the $(A_k,q)$ plane. Colored regions indicate parametric resonance ($\mathrm{Re}(\mu)>0$); the black contour outlines the instability boundary, and the vertical line marks the $l=2$ resonance center at $A_k=4$.
• Figure 2: Resonance band-map computed from the full equation of motion. The instantaneous growth rate $\mu(\tau,\kappa) \equiv t_1^{-1}\,{\rm d}\ln|\phi(\tau;\kappa)|/{\rm d}\tau$ is derived from numerical solutions of Eq. (\ref{['foeq']}). Stable regions between bands are left blank. Band structures widen and become more visible in the weak-driving regime (lower-left). Broken patterns near $2 \times 10^{3}$ reflect numerical precision limits.
• Figure 3: Parametric Resonance’s impact on the QCD axion relic abundance. Homogeneous misalignment (gray) and resonance-enhanced (red) predictions are shown as bands, with widths reflecting the initial misalignment angle $\theta_0 \in [1,2]$. A benchmark case with $\theta_0=1.3$ is highlighted via solid curves through the band centers. Resonance-enhanced scenarios account for 100% dark matter at axion masses $39~(192)~\mu$eV for $\theta_0=1.3~(2.0)$. For comparison, literature predictions and existing haloscope constraints AxionLimits are overlaid. The lower band (yellow) illustrates the mass-coupling relation across QCD axion models.