Compton scattering with parity violation and polarization of cosmic microwave background

The measurement of the polarization of cosmic microwave background (CMB) provides considerable useful information about different physical phenomena at the last scattering surface. The polarization of CMB is due to Compton scattering. In this work, we consider the parity violation of Compton scattering. Then we insert the new amplitude into the quantum Boltzmann equation and show that the forward scattering term can produce the B-mode polarization