Axion-Photon Conversion in FLRW with Primordial Magnetic Fields: Explaining the Radio Excess

Abstract: We explore the possibility of axion-photon conversion as a common origin of two low-frequency anomalies: the isotropic radio excess (ARCADE2) and the deep global 21-cm absorption trough (EDGES). From the axion-photon action in an FLRW background with primordial magnetic fields (PMFs), we derive the scale-dependent conversion probability including plasma effects. Resonant conversion, arising when the axion mass matches the plasma-induced photon mass, produces soft photons in the MHz-GHz range. By modeling stochastic PMFs with amplitude $B_0$ and spectral index $n_{\rm B}$, we show that axion-like particles with mass $\sim 10^{-14}$-$10^{-12}\,\mathrm{eV}$ and nanogauss-level nearly scale invariant PMFs can explain both ARCADE2 and EDGES. Heating from PMF dissipation via ambipolar diffusion and turbulent decay reduces the 21-cm trough, shifting the viable parameter space. Our results stem from a consistent theoretical framework developed from first principles and a combined analysis of the radio excess and global 21-cm signal, while remaining consistent with CMB bounds on PMFs and $\Delta N_{\rm eff}$. We conclude that global 21-cm observations may offer potential sensitivity to axions, primordial magnetism, and dark-sector physics.