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 $L_{\mathrm{G}}^{\mathrm{p}\mathrm{h}\mathrm{y}\mathrm{s}}=\sqrt{6}\mathrm{/}(m_a{v}_a)$, 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 $g_{a\gamma }\sqrt{{\mathrm{\Omega }}_a\mathrm{/}{\mathrm{\Omega }}_{\mathrm{D}\mathrm{M}}}$. For a fiducial survey with ${10}^6$ polarized galaxies over a quarter of the sky to $z=2$ and effective per-galaxy scatter ${\sigma }_{\mathrm{t}\mathrm{o}\mathrm{t}}={10}^{\circ }$, we find $5\sigma$ sensitivity to sub-degree correlated rotations over $m_a({10}^{-3}c\mathrm{/}{v}_a)\sim {10}^{-29}$–${10}^{-27}\mathrm{e}\mathrm{V}$, with $\sigma [{\log }_{10}(m_a{v}_a)]\lesssim 0.1$ for detected signals across much of this range. This provides a geometric late-time probe complementary to CMB birefringence and structure-formation constraints.