Non-Uniform Cosmological Birefringence and Active Galactic Nuclei

Abstract

Cosmological birefringence, a rotation by an angle $\alpha$ of the polarization of photons as they propagate over cosmological distances, is constrained by the cosmic microwave background (CMB) to be $|\alpha |\lesssim 1^{\circ }$ ($1\sigma$) out to redshifts $z\simeq 1100$ for a rotation that is uniform across the sky. However, the rotation angle $\alpha (\theta ,\varphi )$ may vary as a function of position $(\theta ,\varphi )$ on the sky. Here I discuss how a position-dependent rotation can be sought in current and future AGN data. An upper limit $\text{VEV}{{\alpha }^2}^{1/2}\lesssim 3.7^{\circ }$ 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 $(4\pi {)}^{-1/2}{\alpha }_{lm}\lesssim 3.7^{\circ }$ 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 analogous to that used in CMB polarization and weak gravitational lensing.

Comments: 5 pages.