Spin Hall effect of light in inhomogeneous axion field

We study the spin transport of light in weakly inhomogeneous axion field in a flat Robertson-Walker universe and derive the spin Hall effect for circularly polarized rays. Regarding primordial quantum fluctuations of the axion field in the de Sitter phase as the origin of the inhomogeneity, we show that the conformal invariance of the correlator determines the root-mean-square (r.m.s) fluctuations of the path of circularly polarized cosmic rays. We explain how the r.m.s fluctuations can be experimentally determined.