Non-Uniform Cosmological Birefringence and Active Galactic Nuclei

Cosmological birefringence, a rotation by an angle $α$ of the polarization of photons as they propagate over cosmological distances, is constrained by the cosmic microwave background (CMB) to be $|α|\lesssim1^\circ$ ($1σ$) out to redshifts $z\simeq1100$ for a rotation that is uniform across the sky. However, the rotation angle $α(θ,ϕ)$ may vary as a function of position $(θ,ϕ)$ on the sky. Here I discuss how a position-dependent rotation can be sought in current and future AGN data. An upper limit $\VEV{α^2}^{1/2} \lesssim 3.7^\circ$ to the scatter in the position-angle--polarization offsets in a sample of only N=9 AGN already constrains the rotation spherical-harmonic coefficients to $(4π)^{-1/2} α_{lm}\lesssim 3.7^\circ$ 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 analogous to that used in CMB polarization and weak gravitational lensing.

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