Non-Uniform Cosmological Birefringence and Active Galactic Nuclei

TL;DR

This paper explores how spatial variations in cosmological birefringence can be constrained using active galactic nuclei (AGN) polarization data, extending previous uniform rotation limits to position-dependent models.

Contribution

It introduces methods to constrain non-uniform birefringence using AGN polarization data and discusses how future observations can improve these constraints.

Findings

Current AGN data limit the birefringence scatter to about 3.7 degrees.

Constraints on spherical-harmonic coefficients of the rotation field are established.

Future analyses with more sources can significantly tighten these constraints.

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 $|\alpha|\lesssim1^\circ$ ($1\sigma$) out to redshifts $z\simeq1100$ for a rotation that is uniform across the sky. However, the rotation angle $\alpha(\theta,\phi)$ may vary as a function of position $(\theta,\phi)$ on the sky. Here I discuss how a position-dependent rotation can be sought in current and future AGN data. An upper limit $\VEV{\alpha^2}^{1/2} \lesssim 3.7^\circ$ 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.