CMB Mode Coupling with Isotropic Polarization Rotation

TL;DR

This paper introduces a new method to measure isotropic polarization rotation in the CMB by analyzing mode coupling, providing a complementary approach to existing $EB$ spectrum techniques for future high-sensitivity experiments.

Contribution

The paper derives a new mode coupling contribution caused by parity violation from isotropic polarization rotation, enabling alternative constraints on the polarization angle.

Findings

Constraints are comparable to $EB$ spectrum methods.

The technique offers a cross-check for polarization angle measurements.

Applicable to future experiments like CMB-S4 and LiteBIRD.

Abstract

We provide a new analysis technique to measure the effect of the isotropic polarization rotation, induced by e.g. the isotropic cosmic birefringence from axion-like particles and a miscalibration of CMB polarization angle, via mode coupling in the cosmic microwave background (CMB). Several secondary effects such as gravitational lensing and CMB optical-depth anisotropies lead to mode coupling in observed CMB anisotropies, i.e., non-zero off-diagonal elements in the observed CMB covariance. To derive the mode coupling, however, we usually assume no parity violation in the observed CMB anisotropies. We first derive a new contribution to the CMB mode coupling arising from parity violation in observed CMB. Since the isotropic polarization rotation leads to parity violation in the observed CMB anisotropies, we then discuss the use of the new mode coupling for constraining the isotropic polarization angle. We find that constraints on the isotropic polarization angle by measuring the new mode-coupling contribution are comparable to that using the $EB$ cross-power spectrum in future high-sensitivity polarization experiments such as CMB-S4 and LiteBIRD. Thus, this technique can be used to cross-check results obtained by the use of the $EB$ cross-power spectrum.