Dark photon dark matter from flattened axion potentials

Abstract

Dark photons can be resonantly produced in the early universe via their coupling to an oscillating axion field. However, this mechanism typically requires large axion--dark photon couplings or some degree of fine-tuning. In this work, we present a new scenario in which efficient dark photon production arises from axion potentials that are shallower than quadratic at large field values. For moderately large initial misalignment angles, the oscillation of the axion field can trigger either efficient dark photon production or strong axion self-resonance via parametric resonance. When self-resonance dominates and disrupts the field's homogeneity, we show that oscillons -- localized, oscillating axion field configurations -- naturally form and can sustain continued dark photon production, provided the coupling is $\gtrsim \mathcal O(1)$. For dark photon mass up to three orders of magnitude below the axion mass, the produced dark photons can account for a significant fraction of the present-day dark matter. We support this scenario with numerical lattice simulations of a benchmark model. Our results further motivate experimental searches for ultralight dark photon dark matter. The simulation code is publicly available at https://github.com/hongyi18/AxionDarkPhotonSimulator.

Figures (9)

• Figure 1: Left: Comparison between the flattened potential in eq. \ref{['pot_phi']} used in this work (blue), the QCD axion potential $V(\phi) = m_\phi^2 f_\phi^2 [1-\cos(\phi/f_\phi)]$ (solid gray), and a quadratic potential $V(\phi) = m_\phi^2 \phi^2/2$ (dashed gray). Right: Schematic depiction of an oscillon supported by flattened potentials: a longlived, spatially-localized, oscillating field configuration. The field maintains an approximately constant amplitude $\phi_0(t)\sim f_\phi$ within a characteristic radius $R_\mathrm{osc} \simeq \text{a few}\times m_\phi^{-1}$. The oscillon lifetime typically far exceeds $m_\phi^{-1}$ due to suppressed radiation losses.
• Figure 2: Schematic illustration of dark photon production from an oscillating axion field. Initially, the homogeneous axion undergoes parametric resonance, leading to the exponential growth of axion perturbations and transverse dark photon modes within broad instability bands. The dominant growth channel depends on the axion–dark photon coupling, the initial misalignment angle, and the relative amplitudes of axions and gauge field fluctuations. If axion self-resonance dominates, the system can fragment into localized, longlived oscillons, which could sustain continued dark photon production through parametric resonance in narrower instability bands.
• Figure 3: Instability diagram for transverse dark photon modes $X_\pm(t,k)$ in flat spacetime, where $\phi_0$ is the oscillation amplitude of the axion field and $H_\mathrm{osc}$ is the Hubble parameter at the onset of oscillations, defined in eq. \ref{['eq:condition']}. The mode $X_\pm(t,k)$ evolves according to eq. \ref{['floquet_exponent']} and can grow exponentially if $\mathrm{Re}[\mu_k]\neq 0$. In an expanding universe, the instantaneous growth rate $\mathrm{Re}[\mu_k]$ competes with the Hubble dilution rate $H(t)$. As the universe expands, the physical wavenumber evolves as $k/a$, the amplitude of axion oscillations decreases as $\phi_0\propto a^{-3/2}$, and the Hubble parameter decreases as $H\propto a^{-2}$ during radiation domination. Here the dark photon mass is set to $m_X=0.1\,m_\phi$.
• Figure 4: Left: Evolution of the energy densities of axions (blue) and dark photons (orange) for different values of the coupling constant $\alpha$, normalized to the energy density $\rho_{\phi, 0}$ of a homogeneous axion field with zero coupling. The efficiency of broad resonance decreases for smaller $\alpha$. Right: Spectral number densities of axions (blue) and dark photons (orange) as functions of the comoving wavenumber $k$ for $\alpha=5$ at different times. After the resonance saturates, the dark photon spectrum peaks at physical wave number $k_\mathrm{phys}\sim 0.2\,m_\phi$, corresponding to the instability band for $\alpha\phi_0 \sim f_\phi$ in figure \ref{['fig:instabilitychartvector']}. In both panels, the initial conditions are set to $\phi_0=5f_\phi$, $\delta \phi=0$, and $\delta X_i\sim 10^{-35}\phi_0$. The initial scale factor $a_i$ corresponds to the time when $H=10\,m_\phi$.
• Figure 5: Left: Evolution of the energy densities of axions (blue) and dark photons (orange) for different initial amplitudes $\delta X_i$ of the dark photon field, using the same normalization as in figure \ref{['fig:noscatinyvecfluc_density_evol']}. The efficiency of broad resonance decreases with smaller initial fluctuations in the dark photon field. Right: Spectral number densities of axions (blue) and dark photons (orange) at $a/a_i=196$, for different initial amplitudes of the dark photon field. For larger initial fluctuations $\delta X_i \sim 10^{-5}\,\phi_0$, the resonance is primarily driven by the regime $\alpha \phi_0 \gg f_\phi$, where the instability band remains broad, as shown in figure \ref{['fig:instabilitychartvector']}; the resulting dark photon spectrum is less peaked. In both panels, the initial conditions and the coupling constant are set to $\phi_0=5f_\phi$, $\delta \phi=0$, and $\alpha=5$.