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 G 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 a/ 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 tot=10, we find 5 sigma sensitivity to sub-degree correlated rotations over m a(10-3c/v a) about10-29 -- 10-27, eV, with sigma[10(m a v a)] 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.