Generation of circular polarization of CMB due to the Euler-Heisenberg Lagrangian

Abstract

It is known that the dominant contribution of primordial anisotropies of Cosmic Microwave Background (CMB) is linearly polarized via Compton scattering. However circular polarization of this anisotropy has not been observed up to now, but it has not been excluded in observational evidence. Here we show that the Euler-Heisenberg Effective Lagrangian can generate circular polarization in CMB. This generation is calculated by using the Quantum Boltzmann Equation for the time evolution of the Stokes parameter. Also, we estimate the Faraday conversion phase in order of $10^{-13} $ due to this Lagrangian which gives a lower bound on circular polarization of CMB.