Planck constraints on the scale dependence of isotropic cosmic birefringence

The rotation of the linear polarisation plane of photons during propagation, also known as cosmic birefringence, is a powerful probe of parity-violating extensions of standard electromagnetism. Using Planck legacy data, we confirm previous estimates of the isotropic birefringence angle, finding $\beta \simeq 0.30 \pm 0.05$ [deg] at 68% CL, not including the systematic error from the instrumental polarisation angle. If this is a genuine signal, it could be explained by theories of Chern--Simons-type coupled to electromagnetism, which could lead to a harmonic scale-dependent birefringence signal, if the hypothesis of an ultra-light (pseudo) scalar field does not hold. To investigate these models, we pursue two complementary approaches: first, we fit the birefringence angle estimated at different multipoles, $\beta_{\ell}$, with a power-law model and second, we perform a non-parametric Bayesian reconstruction of it. Both methods yield results consistent with a non-vanishing constant birefringence angle. The first method shows no significant dependence on the harmonic scale (up to $1.8\sigma$ CL), while the second method demonstrates that a constant model is favored by Bayesian evidence. This conclusion is robust across all four published Planck CMB solutions. Finally, we forecast that upcoming CMB observations by Simons Observatory, LiteBIRD and a wishful CMB-Stage 4 experiment could reduce current uncertainties by a factor of approximately 7.