Detailed measurements of the CMB lensing signal are an important scientific goal of ongoing ground-based CMB polarization experiments, which are mapping the CMB at high resolution over small patches of the sky. In this work we simulate CMB polarizati
on lensing reconstruction for the $EE$ and $EB$ quadratic estimators with current-generation noise levels and resolution, and show that without boundary effects the known and expected zeroth and first order $N^{(0)}$ and $N^{(1)}$ biases provide an adequate model for non-signal contributions to the lensing power spectrum estimators. Small sky areas present a number of additional challenges for polarization lensing reconstruction, including leakage of $E$ modes into $B$ modes. We show how simple windowed estimators using filtered pure-$B$ modes can greatly reduce the mask-induced mean-field lensing signal and reduce variance in the estimators. This provides a simple method (used with recent observations) that gives an alternative to more optimal but expensive inverse-variance filtering.
We relate the observable number of sources per solid angle and redshift to the underlying proper source density and velocity, background evolution and line-of-sight potentials. We give an exact result in the case of linearized perturbations assuming
general relativity. This consistently includes contributions of the source density perturbations and redshift distortions, magnification, radial displacement, and various additional linear terms that are small on sub-horizon scales. In addition we calculate the effect on observed luminosities, and hence the result for sources observed as a function of flux, including magnification bias and radial-displacement effects. We give the corresponding linear result for a magnitude-limited survey at low redshift, and discuss the angular power spectrum of the total count distribution. We also calculate the cross-correlation with the CMB polarization and temperature including Doppler source terms, magnification, redshift distortions and other velocity effects for the sources, and discuss why the contribution of redshift distortions is generally small. Finally we relate the result for source number counts to that for the brightness of line radiation, for example 21-cm radiation, from the sources.
Beam asymmetries result in statistically-anisotropic cosmic microwave background (CMB) maps. Typically, they are studied for their effects on the CMB power spectrum, however they more closely mimic anisotropic effects such as gravitational lensing an
d primordial power asymmetry. We discuss tools for studying the effects of beam asymmetry on general quadratic estimators of anisotropy, analytically for full-sky observations as well as in the analysis of realistic data. We demonstrate this methodology in application to a recently-detected 9 sigma quadrupolar modulation effect in the WMAP data, showing that beams provide a complete and sufficient explanation for the anomaly.
