Measuring Ultralight-Axion Coherence with Galaxy Polarization Correlations

Abstract

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 $L_{\mathrm{G}}^{\mathrm{phys}}=\sqrt{6}/(m_a{v}_a)$, 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 $g_{a\gamma }\sqrt{{\Omega }_a/{\Omega }_{\mathrm{DM}}}$. For a fiducial survey with $10^6$ polarized galaxies over a quarter of the sky to $z=2$ and effective per-galaxy scatter ${\sigma }_{\mathrm{tot}}=10^{\circ }$, we find $5\sigma$ sensitivity to sub-degree correlated rotations over $m_a(10^{-3}c/v_a)\sim 10^{-29}$--$10^{-27}\mathrm{eV}$, 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.

arXiv commentThe author is withdrawing this manuscript because its key predictions, namely a 5σ detection and a 0.1 dex precision constraint on ultralight axion coherence, cannot be adequately substantiated under realistic observational conditions. These predictions rely on idealized assumptions, and the calculations do not provide sufficient support for the claimed observational sensitivity