Impact of Anisotropic Birefringence on Measuring Cosmic Microwave Background Lensing

The power spectrum of cosmic microwave background lensing is a powerful tool for constraining fundamental physics such as the sum of neutrino masses and the dark energy equation of state. Current lensing measurements primarily come from distortions to the microwave background temperature field, but the polarization lensing signal will dominate upcoming experiments with greater sensitivity. Cosmic birefringence refers to the rotation of the linear polarization direction of microwave photons propagating from the last scattering surface to us, which can be induced by parity-violating physics such as axion-like dark matter or primordial magnetic fields. We find that, for an upcoming CMB-S4-like experiment, if there exists the scale-invariant anisotropic birefringence with an amplitude corresponding to the current $95\%$ upper bound, the measured lensing power spectrum could be biased by up to a factor of few at small scales, $L\gtrsim 1000$. We show that the bias scales linearly with the amplitude of the scale-invariant birefringence spectrum. The signal-to-noise of the contribution from anisotropic birefringence is larger than unity even if the birefringence amplitude decreases to $\sim 5\%$ of the current upper bound. Our results indicate that a measurement and characterization of the anisotropic birefringence is important for lensing analysis in future low-noise polarization experiments.