Polarization of the CMB in the Standard Model Extension

TL;DR

The paper investigates whether Lorentz-violating operators in the SME photon sector can generate circular polarization and cosmic birefringence in the CMB. By formulating the Boltzmann evolution of the Stokes parameters with CPT-odd $K_{AF}$ and CPT-even $K_{F}$ terms, it derives a nonzero Faraday-conversion effect that converts linear polarization into circular polarization, yielding a bound $k_{AF} \sim 10^{-41}$ GeV. In the combined LV analysis, it links CB to the $K_{F}$ term and obtains a tighter bound $K_{F} \sim 10^{-32}$ GeV from best-fitting CB angles, improving on prior limits. These results constrain SME photon-sector LV and inform future CMB polarization observations (e.g., CMB-S4, Simons Observatory, PICO) aimed at detecting or further limiting LV signatures in the early universe.

Abstract

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} $.