Cosmic Birefringence: going beyond linear-order in perturbation theory

This thesis studies Cosmic Birefringence (CB), the rotation of the polarization plane of the Cosmic Microwave Background (CMB) caused by a Chern-Simons correction to the Maxwell Lagrangian, whose coupling is promoted to be a function of an axion-like particle (ALP). This ALP, denoted as $\chi$ can act as dark matter or early dark energy depending on its potential and mass (and is well motivated in different contexts, e.g. string theory). The parity-violating rotation of the CMB $E$- and $B$-modes produces $EB$ and $TB$ cross-correlations forbidden in a parity-conserving theory. This thesis focuses on the so-called “\emph{anisotropic}” Cosmic Birefringence $\delta\alpha(\hat{\mathbf{n}})$, the space-dependent deviations from the mean birefringence angle $\alpha_0$, arising from the spatial fluctuations of the ALP. Existing calculations of three-point angular correlations between $\delta\alpha$ and observed CMB maps show that, even assuming Gaussian fields and no primordial cross-correlation, non-zero observed bispectra arise. This motivates also including primordial three-point correlations, induced from primordial non-Gaussianity (PNG), since their contribution is of the same perturbative order, a computation of the corrections from PNG to the $\delta\alpha$–CMB power spectra and bispectra is performed. The PNG-induced terms are derived and show that they give significant contributions to both power spectra and bispectra. For the first time, we show how a cross-correlation between $\delta\alpha(\hat{\mathbf{n}})$ and the $B$-modes of polarization (which has already been observationally constrained ) can arise by considering the PNG-induced three-point primordial correlations. Finally, PNG-induced cross-correlations between the CMB and $\delta\alpha$ define a new class of observational probes to constrain primordial non-Gaussianity.