Cosmic Birefringence with the Cosmic Microwave Background: A Harmonic-Based Methodology

This thesis explores parity-violating extensions of standard electromagnetism, which can be realized through a Chern-Simons term coupling the dual of the electromagnetic tensor to a scalar field (or pseudo-scalar field, such as an axion-like field) where the latter may act as dark matter or dark energy. This interaction rotates the linear polarization of light in a manner similar to birefringent materials and is therefore commonly referred to as the Cosmic Birefringence (CB) effect. Since the Cosmic Microwave Background (CMB) is linearly polarized due to Thomson scattering at the last scattering surface, the CMB is often used to probe this phenomenon. In fact, recent analyses on Planck data, have intriguingly hinted at a detection of CB with a statistical significance ranging from 2.4 to 3.6 sigma. These measurements have attracted significant attention in recent years, as they hold the potential to uncover new physics beyond the standard model of particle physics and cosmology. In this thesis, we compute how CB affects the CMB angular power spectra. Additionally, we analytically derive two harmonic-based estimators, known in the literature as D-estimators, which constrain the CB effect by utilizing information from the TB (temperature anisotropies and B-mode polarization) and EB (E- and B-mode polarization) CMB angular power spectra. We verify that these estimators correctly recover the birefringence angle and assess their expected statistical efficiency, recovering known results from the literature. Additionally, we perform a detailed analysis of the joint estimator, obtained by combining the two D-estimators, and provide an analytical expression for the total joint uncertainty. While it is known that the joint estimator is dominated by the one derived from the EB spectrum, the final expression for the combined estimator can be considered new.