CMB beam systematics: Impact on lensing parameter estimation

Abstract

The cosmic microwave background (CMB) is a rich source of cosmological information. Thanks to the simplicity and linearity of the theory of cosmological perturbations, observations of the CMB's polarization and temperature anisotropy can reveal the parameters that describe the contents, structure, and evolution of the cosmos. Temperature anisotropy is necessary but not sufficient to fully mine the CMB of its cosmological information as it is plagued with various parameter degeneracies. Fortunately, CMB polarization breaks many of these degeneracies and adds new information and increased precision. Of particular interest is the CMB's $B$-mode polarization, which provides a handle on several cosmological parameters most notably the tensor-to-scalar ratio $r$ and is sensitive to parameters that govern the growth of large-scale structure and evolution of the gravitational potential. These imprint CMB temperature anisotropy and cause $E$-to-$B$-mode polarization conversion via gravitational lensing. However, both primordial gravitational-wave- and secondary lensing-induced $B$-mode signals are very weak and therefore prone to various foregrounds and systematics. In this work we use Fisher-matrix-based estimations and apply, for the first time, Monte Carlo Markov Chain simulations to determine the effect of beam systematics on the inferred cosmological parameters from five upcoming experiments: PLANCK, POLARBEAR, SPIDER, $\mathrm{QUIET}+\mathrm{CLOVER}$, and CMBPOL. We consider beam systematics that couple the beam substructure to the gradient of temperature anisotropy and polarization (differential beamwidth, pointing offsets and ellipticity) and beam systematics due to differential beam normalization (differential gain) and orientation (beam rotation) of the polarization-sensitive axes (the latter two effects are insensitive to the beam substructure). We determine allowable levels of beam systematics for given tolerances on the induced parameter errors and check for possible biases in the inferred parameters concomitant with potential increases in the statistical uncertainty. All our results are scaled to the ``worst case scenario.'' In this case, and for our tolerance levels the beam rotation should not exceed the few-degree to subdegree level, typical ellipticity is required to be 1%, the differential gain allowed level is a few parts in ${10}^{3}$ to ${10}^{4}$, differential beam width upper limits are of the subpercent level, and differential pointing should not exceed the few- to sub-arc sec level.