Abstract

Polarization of the cosmic microwave background (CMB) can help probe cosmic inflation (via the measurement of primordial B modes) and test parity-violating physics (via the detection of cosmic birefringence). These promising opportunities are driving the development of a number of new ground-based, balloon-borne and space-based CMB experiments. However, for these ambitious missions to be successful, systematic effects must be precisely controlled and accurately mitigated. To this end, some next-generation CMB experiments (including LiteBIRD) will use rotating half-wave plates (HWPs) as polarization modulators. Ideally, this choice should completely remove the 1/f noise component in the observed polarization and reduce the intensity-to-polarization leakage, thus mitigating two important systematic effects. However, any real HWP is characterized by non-idealities which, if not properly treated in the analysis, can lead to additional systematics. In this thesis, after briefly introducing the science case, we discuss the macro steps that make up any CMB experiment, introduce the HWP, and present a new time-ordered data (TOD) simulation pipeline tailored to a LiteBIRD-like experiment that can return TOD and binned maps for realistic beams and HWPs. We show that the simulation framework can be used to study how the HWP non-idealities affect the measured cosmic birefringence angle, resulting in a bias of a few degrees for a realistic choice of HWP. We also derive analytical formulae that model the observed temperature and polarization maps and test them against the output of the simulation. Finally, we present a simple, semi-analytical end-to-end model to propagate the HWP non-idealities through the macro-steps that make up any CMB experiment (observation of multi-frequency maps, foreground cleaning, and power spectra estimation) and compute the HWP-induced bias on the estimated tensor-to-scalar ratio, r, finding that the HWP leads to an underestimation of r. We also show how gain calibration of the CMB temperature can be used to partially mitigate the non-idealities' impact and present a set of recommendations for the HWP design that can help maximize the benefits of gain calibration.