Nonuniform cosmological birefringence and active galactic nuclei

The CMB constrains the cosmological-birefringence rotation angle to be |α|≲1° (1σ) out to redshifts z≃1100 for a rotation that is uniform across the sky. However, the rotation angle α(θ,ϕ) may vary with position (θ,ϕ) on the sky, and if so, then it can be sought in current and future future active galactic nuclei data. An upper limit ^(1/2)≲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 (4π)^(-1/2)α_(lm)≲3.7° and constrains the power spectrum for α 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.