Cosmic Birefringence Reloaded: an assessment of present models

Cosmic birefringence, the rotation of the linear polarization of electromagnetic radiation during propagation, provides a sensitive probe of parity-violating physics beyond the standard cosmological model. In this thesis, cosmic birefringence is investigated in the framework of an axion-like pseudoscalar field coupled to electromagnetism through a Chern–Simons interaction. The homogeneous and perturbed dynamics of the field are studied with the aim of connecting its cosmological evolution to both isotropic and anisotropic birefringence of the Cosmic Microwave Background (CMB). The theoretical analysis begins with the dynamics of the pseudoscalar field in an expanding Universe, with particular emphasis on the transition between the slow-roll and oscillatory regimes. Four potentials for the scalar field are considered: quadratic, cosine, quartic monomial (Rock `n' Roll), and squared cosine. Their effective cosmological behavior is reviewed, showing that oscillating fields can reproduce matter-like or radiation-like dilution depending on the shape of the potential. The dynamics of the field's linear perturbations are then derived explicitly, constituting an important piece in the development of a gauge-invariant description of curvature and entropy perturbations. An extension of the matrix formalism for a scalar field chi coupled to a perfect fluid f is constructed to accommodate a more realistic multi-fluid cosmological background. The connection between the pseudoscalar field and CMB polarization is subsequently established through the rotation of the Stokes parameters and the resulting mixing of E and B mode polarization. This provides the theoretical basis for relating the field excursion between photon emission and observation to an observable birefringence angle. A modified version of the Cosmic Linear Anisotropy Solving System (CLASS) is then employed to investigate the background evolution of the four potentials. Bayesian inference is used to identify combinations of the pseudoscalar mass m_chi and photon coupling g capable of reproducing a birefringence angle of the magnitude reported by recent CMB analyses, while satisfying the relevant cosmological and axion-photon coupling constraints. The results show that the inferred parameter relations depend sensitively on the potential, on the initial conditions at the starting redshift of the simulation (z=10^14), and on the impact of the field on today's energy density fraction. Fields exhibiting radiation-like behavior during the oscillatory phase are shown to permit higher masses in parameter space than their matter-like counterparts. The corresponding gauge-invariant entropy perturbations are also evolved on super-horizon scales using the background solutions obtained from CLASS. In all the representative cases we studied, the entropy perturbations decay strongly, while the curvature perturbation R remains approximately constant once the initial transient evolution has passed. These results provide a consistency check for the considered birefringence-producing backgrounds, although a complete treatment of the perturbations and their observational signatures remains beyond the scope of the present work. Regardless of the chosen potential, each contour in (m_chi,g) parameter space shows two distinct regions: a solid line for lighter masses and a characteristic "patchy" appearance for heavier ones; the latter feature appears for ALPs that are massive enough to exit their frozen state early and oscillate appreciably around the recombination epoch. In the first region, the polarization axis of all electromagnetic radiation is subjected to a uniform rotation, while in the second the impact of cosmic birefringence can vary significantly depending on the amplitude of chi at the exact time of the photon's last scattering.[...]