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

Abstract

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 $A^{αα} < 0.104 \, \mbox{[deg$^2$]}$ and $A^{αT}=1.50^{+2.41}_{-4.10} \, \mbox{[$μ$K$\cdot$deg] both at } 95 \% \mbox{ C.L.}$. The latter bound appears competitive in constraining a few early dark energy models recently proposed to alleviate the $H_0$ tension. Slicing the joint likelihood at $A^{\alpha T}=0$, the bound on $A^{\alpha \alpha }$ becomes tighter at $A^{αα} < 0.085 \, \mbox{[deg$^2$]}$ at 95$\% \mbox{ C.L.}$. In addition we recast the constraints on $A^{\alpha \alpha }$ as a bound on the amplitude of primordial magnetic fields responsible for Faraday rotation, finding $B_{1 {\tiny \mbox{Mpc}}} < 26.9$ nG and $B_{1 {\tiny \mbox{Mpc}}} < 24.3$ nG at 95$\%$ C.L. for the marginalised and sliced case respectively.

38 pages, 34 Figures. References added. Section 6 extended. Accepted for publication in Journal of Cosmology and Astroparticle Physics