Analytic Approach to CMB Beam Systematics: Effect on Inflation Science, Lensing Extraction and Cosmic Birefringence

The CMB’s B-mode polarization provides a handle on several cosmological parameters most notably the tensor-to-scalar ratio, r, and is sensitive to parameters which govern the growth of large scale structure (LSS) and evolution of the gravitational potential. These imprint CMB temperature anisotropy and cause E-to-B-mode polarization conversion via gravitational lensing. The CMB has also the potential to constrain departures from standard electromagnetism and gravitation for which the ‘forbidden’ TB and EB correlations are unique ‘smoking guns’. However, both primordial gravitational-wave and secondary lensing-induced B-mode signals, as well as the upper limits on TB and EB are very weak and therefore prone to various foregrounds and systematics. In this summary we concisely describe an analytic approach to beam systematics which allows a fast and accurate determination of various beam systematics in certain idealized cases this tool is particularly useful in the design-phase of CMB experiments like CMBPOL when forecasts of the expected science-return are being made. We also discuss the issue of scanning strategy as a mitigation tool and propagate beam systematics to parameter estimation to determine tolerances on the allowed beam parameters.