Primordial Gravitational Waves and Rescattered Electromagnetic Radiation in the Cosmic Microwave Background

TL;DR

This paper explores how primordial gravitational waves can induce a unique polarization pattern in the CMB through rescattering of electromagnetic radiation by charges, offering a new perspective on GW-CMB interactions.

Contribution

It introduces a novel effect where GWs cause polarization in the CMB via rescattering, which has not been previously analyzed in this context.

Findings

Rescattered EM radiation exhibits net linear polarization.

Polarization patterns can be represented as E- and B-modes.

The polarization effect does not directly reflect GW properties.

Abstract

Understanding the interaction of primordial gravitational waves (GWs) with the Cosmic Microwave Background (CMB) plasma is important for observational cosmology. In this article, we provide an analysis of an effect apparently overlooked as yet. We consider a single free electric charge and suppose that it can be agitated by primordial GWs propagating through the CMB plasma, resulting in periodic, regular motion along particular directions. Light reflected by the charge will be partially polarized, and this will imprint a characteristic pattern on the CMB. We study this effect by considering a simple model in which anisotropic incident electromagnetic (EM) radiation is rescattered by a charge sitting in spacetime perturbed by GWs and becomes polarized. As the charge is driven to move along particular directions, we calculate its dipole moment to determine the leading-order rescattered EM radiation. The Stokes parameters of the rescattered radiation exhibit a net linear polarization. We investigate how this polarization effect can be schematically represented out of the Stokes parameters. We work out the representations of gradient modes (E-modes) and curl modes (B-modes) to produce polarization maps. Although the polarization effect results from GWs, we find that its representations, the E- and B-modes, do not practically reflect the GW properties such as strain amplitude, frequency and polarization states.