Generation of circular polarization of CMB from the Euler–Heisenberg Lagrangian

Abstract

It is known that the dominated contribution of primordial anisotropies of cosmic microwave background (CMB) are 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 evidences. Here we show that the Euler–Heisenberg effective Lagrangian can generate circular polarization in CMB. This generation is calculated by using the quantum Boltzman equation for time evolution of the Stokes parameter. Also we estimate Faraday conversion phase on the order of 10−13 due to this Lagrangian, which gives a lower bound on circular polarization of CMB.