General Relativistic Contribution to Polarization of the Cosmic Microwave Background Anisotropy

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 ∆V , is however very small compared to the linear polarisation caused by Thomson scattering. In the standard treatment of the microwave background anisotropies [1] it is assumed that the gravitational potential at the last scattering surface gives rise to temperature anisotropies at large angular scales through the Sachs-Wolfe effect [2]. Thomson scatterings near the surface of last scattering cause a linear polarisation of the CMB photons. The anisotropies of CMBR are governed by the the following set of equations: The Boltzmann equation for the photon ditribution function f(pi, p0, z) Df Dλ = p ∂f ∂x0 + p ∂f ∂xi + dp dλ ∂f ∂pi = 0 (1) the geodesic equation of photons in the perturbed metric dp dλ + Γβγp p = 0 (2) and the photon disperison relation