Measuring Ultralight-Axion Coherence with Galaxy Polarization Correlations

Ultralight axion-like particles coupled to photons rotate the linear polarization of distant sources. We propose using the three-dimensional two-point correlation of galaxy polarization-rotation angles to measure not only the amplitude of this birefringence field but also its spatial coherence scale. For a nonrelativistic ALP component with an isotropic Gaussian velocity distribution, the equal-time field correlation has an $e^{-1}$ scale $L_{\rm G}^{\rm phys}=\sqrt{6}/(m_a v_a)$, where $v_a$ is the three-dimensional rms ALP velocity dispersion. A detected turnover in the galaxy-pair correlation therefore measures the characteristic momentum scale $m_a v_a$, while the correlation amplitude constrains $g_{a\gamma}\sqrt{\Omega_a/\Omega_{\rm DM}}$. For a fiducial survey with $10^6$ polarized galaxies over a quarter of the sky to $z=2$ and effective per-galaxy scatter $\sigma_{\rm tot}=10^\circ$, we find $5\sigma$ sensitivity to sub-degree correlated rotations over $m_a(10^{-3}c/v_a)\sim10^{-29}$--$10^{-27}\,{\rm eV}$, with $\sigma[\log_{10}(m_a v_a)]\lesssim0.1$ for detected signals across much of this range. This provides a geometric late-time probe complementary to CMB birefringence and structure-formation constraints.