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 $g_{a{\hat{I}}^3}\sqrt{\hat{I}{\text{c◯}}_a/\hat{I}{\text{c◯}}_{\mathrm{DM}}}$. For a fiducial survey with $10^6$ polarized galaxies over a quarter of the sky to $z=2$ and effective per-galaxy scatter $\ddot{I}{ƒ}_{\mathrm{tot}}=10^{\circ }$, we find $5\ddot{I}ƒ$ sensitivity to sub-degree correlated rotations over $m_a(10^{-3}c/v_a)\sim 10^{-29}$--$10^{-27}\mathrm{eV}$, with $\ddot{I}ƒ[{\log }_{10}(m_a{v}_a)]\lesssim 0.1$ for detected signals across much of this range. This provides a geometric late-time probe complementary to CMB birefringence and structure-formation constraints.

4 pages, 2 figures

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