The Impact of Axion Fields on CMB Polarization through the Cosmic Birefringence Effect: A Numerical Study

Cosmic birefringence denotes a parity-violating modification of the propagation of electromagnetic radiation over cosmological distances. In such a scenario, the polarisation eigenstates of light acquire different phases during propagation, so that photons behave as if they were traveling through a birefringent medium. The observable consequence is an accumulated rotation of the linear polarisation direction. In the context of Cosmic Microwave Background (CMB) photons, this rotation mixes E and B modes and can generate the parity-odd spectra TB and EB, thereby making cosmic birefringence a sensitive probe of physics beyond the standard parity-conserving cosmological model. This thesis studies the case in which the birefringent effect is induced by an axion-like pseudo-scalar field coupled to electromagnetism through a Chern–Simons interaction. The main goal of this work is to build and validate an independent numerical framework for axion-induced cosmic birefringence within a Boltzmann-code setting. A modified version of CLASS is developed to evolve the homogeneous axion background and its perturbations, compute the isotropic rotation angles associated with recombination and reionisation, and predict the anisotropic rotation spectra Cαα ℓ , CαT ℓ , and CαE ℓ . The calculation is then connected to the observable CMB spectra through a post-processing rotation pipeline, including the parity-odd channels EB and TB. The implementation is validated against an independent modified CLASS_BIR calculation. The total anisotropic birefringence spectra agree very well over the harmonic range considered, with the largest residuals appearing in the lightest-mass cases, where the spectra are strongly suppressed and the signed cross-correlations are numerically delicate. The validated code is then used to describe the mass dependence of the signal. The axion mass acts as a clock: it determines when the field leaves the Hubble-frozen regime and therefore which part of the field trajectory is sampled by recombination and reionisation photons. This tomographic information is not captured by a single constant rotation angle. The resulting framework provides the ingredients needed for future likelihood analyses of parity-violating axion physics using CMB polarisation data.