Impact of half-wave plate systematics on the measurement of cosmic birefringence from CMB polarization

Polarization of the cosmic microwave background (CMB) can probe new parity-violating physics such as cosmic birefringence (CB), which requires exquisite control over instrumental systematics. The non-idealities of the half-wave plate (HWP) represent a source of systematics when used as a polarization modulator. We study their impact on the CMB angular power spectra, which is partially degenerate with CB and miscalibration of the polarization angle. We use full-sky beam convolution simulations including HWP to generate mock noiseless time-ordered data, process them through a bin averaging map-maker, and calculate the power spectra including $TB$ and $EB$ correlations. We also derive analytical formulae which accurately model the observed spectra. For our choice of HWP parameters, the HWP-induced angle amounts to a few degrees, which could be misinterpreted as CB. Accurate knowledge of the HWP is required to mitigate this. Our simulation and analytical formulae will be useful for deriving requirements for the accuracy of HWP calibration.