Planck constraints on Cosmic Birefringence and its cross-correlation with the CMB

Cosmic birefringence is the in-vacuo, frequency independent rotation of the polarization plane of linearly polarized radiation, induced by a parity-violating term in the electromagnetic Lagrangian. We implement an harmonic estimator for the birefringence field that only relies on the CMB E to B mode cross-correlation, thus suppressing the effect of cosmic variance from the temperature field. We derive constraints from Planck public releases 3 and 4, revealing a cosmic birefringence power spectrum consistent with zero at about $2\sigma$ up to multipole $L=1500$. Moreover, we find that the cross-correlations of cosmic birefringence with the CMB T-, E- and B-fields are also well compatible with null. The latter two cross-correlations are provided here for the first time up to $L=1500$.