Planck 2018 constraints on anisotropic birefringence and its cross-correlation with CMB anisotropy

Parity-violating extensions of standard electromagnetism produce cosmic birefringence, the in vacuo rotation of the linear polarisation direction of a photon during propagation. We employ Planck 2018 CMB polarised data to constrain anisotropic birefringence, modeled by its angular power spectrum Cℓα α, and the cross-correlation with CMB temperature maps, Cℓα T, at scales larger than ∼15 degrees. We present joint limits on the scale invariant quantity, Aα α ≡ ℓ (ℓ +1) Cℓα α / 2 π, and on the analogous amplitude for the cross-correlation, Aα T ≡ ℓ (ℓ +1) Cℓα T / 2 π. We find no evidence of birefringence within the error budget and obtain Aα α < 0.104 [deg^2] and Aα T=1.50+2.41-4.10 [muKcdotdeg] both at 95 % C.L.. The latter bound appears competitive in constraining a few early dark energy models recently proposed to alleviate the H0 tension. Slicing the joint likelihood at 0Aα T=, the bound on Aα α becomes tighter at Aα α < 0.085 [deg^2] at 95% C.L.. In addition we recast the constraints on Aα α as a bound on the amplitude of primordial magnetic fields responsible for Faraday rotation, finding B1 Mpc < 26.9 nG and B1 Mpc < 24.3 nG at 95% C.L. for the marginalised and sliced case respectively.