New estimators for anisotropic birefringence from CMB observations.

Cosmic birefringence (CB), i.e. the in vacuo rotation of the linear polarisation direction of a photon during propagation, is a tracer for new parity-violating interactions beyond the standard model of particle physics. This phenomenon can be driven by a cosmological pseudoscalar field coupled to the electromagnetism. Several astrophysical sources of linearly polarised photons can be used to investigate this effect. Among these sources, we focus on the oldest one of the Universe, i.e. the Cosmic Microwave Background (CMB) radiation, which is linearly polarised because of Thomson scattering. The CB rotation mixes the Q and U Stokes parameters and consequently the E- and B-mode polarisation. So if it is present this effect turns on the TB and EB cross- correlation between temperature and polarisation CMB power spectra, which are expected to be null in the standard scenario. Note that Cosmic Birefringence can be isotropic, when a single angle is enough to describe the all-sky phenomenon, and anisotropic, when the rotation depends on the direction of observations and therefore the phenomenon will be characterised by a map of angles. Current estimates for both isotropic and anisotropic birefringence are compatible with null effect. However, a recent analysis on Planck 2018 data lead by Minami and Komatsu provides an hint of detection for the isotropic birefringence at the level of 2.4σ.σ. In this talk, after presenting the main equations relating the birefringence effect to the observed CMB angular power spectra, we show how to build harmonic-based estimators sensitive to the features of this phenomenon. Starting from the observed CMB spectra we derive expressions useful to estimate the isotropic birefringence angle, the variance and the angular power spectrum of the birefringence anisotropies. In particular, we present the formalism for a novel statistical technique aimed at estimating the anisotropic birefringence effect from the observed CMB spectra. After a description of the algrebraic properties of this new methodology, we numerically validate the implementation in a Python code with realistic simulations and present preliminary constraints obtained from recent Planck 2018 data.