Detailed study of HWP non-idealities and their impact on future measurements of CMB polarization anisotropies from space

We study the propagation of a specific class of instrumental systematics to the reconstruction of the B-mode power spectrum of the cosmic microwave background (CMB). We focus on the non-idealities of the half-wave plate (HWP), a polarization modulator that is to be deployed by future CMB experiments, such as the phase-A satellite mission LiteBIRD. We study the effects of non-ideal HWP properties, such as transmittance, phase shift, and cross-polarization. To this end, we developed a simple, yet stand-alone end-to-end simulation pipeline adapted to LiteBIRD. We analyzed the effects of a possible mismatch between the measured frequency profiles of HWP properties (used in the mapmaking stage of the pipeline) and the actual profiles (used in the sky-scanning step). We simulated single-frequency, CMB-only observations to emphasize the effects of non-idealities on the BB power spectrum. We also considered multi-frequency observations to account for the frequency dependence of HWP properties and the contribution of foreground emission. We quantified the systematic effects in terms of a bias $\Delta r$ on the tensor-to-scalar ratio, $r$, with respect to the ideal case without systematic effects. We derived the accuracy requirements on the measurements of HWP properties by requiring $\Delta r < 10^{-5}$ (1% of the expected LiteBIRD sensitivity on $r$). Our analysis is introduced by a detailed presentation of the mathematical formalism employed in this work, including the use of the Jones and Mueller matrix representations.