General Relativistic Contribution to Polarization of the Cosmic Microwave Background Anisotropy

TL;DR

This paper investigates how scalar metric perturbations in the universe induce a tiny optical rotation in CMB photons, adding a gravitationally generated polarization component that is much smaller than the Thomson scattering polarization.

Contribution

It provides a detailed solution to the electromagnetic wave equation in a perturbed universe, revealing a gravitationally induced optical rotation effect on CMB polarization.

Findings

Gravitational coupling causes a small optical rotation of CMB photons.

The gravitationally induced V-Stokes parameter anisotropy is negligible compared to Thomson scattering.

Scalar perturbations contribute minimally to CMB polarization rotation.

Abstract

We solve the wave equation for the electromagnetic field tensors associated with the CMBR photons in a universe with scalar metric perturbations. We show that the coupling of the electromagnetic fields with the curvature associated with the scalar perturbations gives rise to an optical rotation of the microwave background photons. The magnitude of the gravitationally generated V-Stokes parameter anisotropy $\Delta_V$, is however very small compared to the linear polarisation caused by Thomson scattering.