Generation of circular polarization in CMB radiation via nonlinear photon-photon interaction

Standard cosmological models do predict a measurable amount of anisotropies in the intensity and linear polarization of the Cosmic Microwave Background radiation (CMB) via Thomson scattering, even though these theoretical models do not predict circular polarization for CMB radiation. In other hand, the circular polarization of CMB has not been excluded in observational evidences. Here we estimate the circular polarization power spectrum $C_{l}^{V(S)}$ in CMB radiation due to Compton scattering and non-linear photon-photon forward scattering via Euler-Heisenberg Effective Lagrangian. We have estimated the average value of circular power spectrum is $1(l+1)\,C_{l}^{V(S)}/(2\pi)\sim 10^{-4}\mu\,K^2$ for $l\sim300$ at present time which is smaller than recently reported data (SPIDER collaboration) but in the range of the future achievable experimental data. We also show that the generation of B-mode polarization for CMB photons in the presence of the primordial scalar perturbation via Euler-Heisenberg interaction is possible however this contribution for B-mode polarization is not remarkable.