Nonuniform cosmological birefringence and active galactic nuclei

The CMB constrains the cosmological-birefringence rotation angle to be $|\alpha |\lesssim 1°$ ($1\sigma$) out to redshifts $z\simeq 1100$ for a rotation that is uniform across the sky. However, the rotation angle $\alpha (\theta ,\varphi )$ may vary with position $(\theta ,\varphi )$ on the sky, and if so, then it can be sought in current and future active galactic nuclei data. An upper limit $⟨{\alpha }^2{⟩}^{1/2}\lesssim 3.7°$ to the scatter in the position-angle–polarization offsets in a sample of only $N=9$ active galactic nuclei already constrains the rotation spherical-harmonic coefficients to $(4\pi {)}^{-1/2}{\alpha }_{lm}\lesssim 3.7°$ and constrains the power spectrum for $\alpha$ in models where it is a stochastic field. Future constraints can be improved with more sources and by analyzing well-mapped sources with a tensor-harmonic decomposition of the polarization.