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

Understand

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 {\it Planck} 2018 CMB polarised data to constrain anisotropic birefringence, modeled by its angular power spectrum $C_{\ell}^{\alpha \alpha}$, and the cross-correlation with CMB temperature maps, $C_{\ell}^{\alpha T}$, at scales larger than $\sim$15 degrees.
• We present joint limits on the scale invariant quantity, $A^{\alpha \alpha} \equiv \ell (\ell +1) \, C_{\ell}^{\alpha \alpha} / 2 \pi$, and on the analogous amplitude for the cross-correlation, $A^{\alpha T} \equiv \ell (\ell +1) \, C_{\ell}^{\alpha T} / 2 \pi$.
• We find no evidence of birefringence within the error budget and obtain $A^{\alpha \alpha} < 0.104 \, \mbox{[deg$^2$]}$ and $A^{\alpha T}=1.50^{+2.41}_{-4.10} \, \mbox{[$\mu$K$\cdot$deg] both at } 95 \% \mbox{ C.L.}$.