Polarization of the CMB in the Standard Model Extension

In standard cosmology, Cosmic Microwave Background photons near the last scattering surface exhibit only linear polarization due to Compton scattering, leading to the assumption that primordial circular polarization is negligible. However, the physics of Lorentz violation (LV), associated with specific operators, can influence these polarization characteristics. This study employs the Boltzmann equation within the framework of the Standard Model Extension (SME) to explore how the background LV tensor $K_{AF}$ can induce circular polarization in CMB radiation. By computing the transformation of linear polarization into circular polarization and utilizing the Faraday conversion angle, we derive a bound for $K_{AF}$ on the order of $10^{-41} \, \text{GeV}$, aligning with recent findings. Additionally, we consider the total pure photon terms within the SME, demonstrating that LV in the presence of scalar perturbations can also generate cosmic birefringence (CB) in the CMB radiation. Through analysis of best-fitting CB angles, we establish a more stringent bound of approximately $10^{-32} \, \text{GeV}$ for $K_{F}$.