Cluster masses from CMB and galaxy weak lensing

Gravitational lensing can be used to directly constrain the projected density profile of galaxy clusters. We discuss possible future constraints using lensing of the cosmic microwave background (CMB) temperature and polarization, and compare to results from using galaxy weak lensing. We model the moving lens and kinetic Sunyaev-Zel'dovich signals that confuse the temperature CMB lensing when cluster velocities and angular momenta are unknown, and show how they degrade parameter constraints. The CMB polarization cluster lensing signal is ~1 μK for massive clusters and challenging to detect; however it should be significantly cleaner than the temperature signal and may provide the most robust constraints at low noise levels. Galaxy lensing is likely to be much better for constraining cluster masses at low redshift, but for clusters at redshift z1 future CMB lensing observations may be able to do better.