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