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

TL;DR

This paper uses Planck 2018 data to set limits on anisotropic cosmic birefringence and its correlation with CMB anisotropies, constraining models of early dark energy and primordial magnetic fields.

Contribution

It provides the first joint constraints on anisotropic birefringence and its cross-correlation with CMB temperature, improving bounds on related cosmological models.

Findings

No evidence of birefringence detected within error margins.

Upper bounds on birefringence amplitude: A^{αα} < 0.104 deg^2.

Constraints on primordial magnetic fields: B_{1 Mpc} < 26.9 nG.

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 $A^{\alpha \alpha} < 0.104 \, \mbox{[deg$^2$]}$ and $A^{\alpha T}=1.50^{+2.41}_{-4.10} \, \mbox{[$\mu$K$\cdot$deg] both at } 95 \% \mbox{ C.L.}$. 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 $A^{\alpha \alpha} < 0.085 \, \mbox{[deg$^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.