Clusters of galaxies are powerful cosmological probes, particularly if their masses can be determined. One possibility for mass determination is to study the cosmic microwave background (CMB) on small angular scales and observe deviations from a pure gradient due to lensing of massive clusters. I show that, neglecting contamination, this technique has the power to determine cluster masses very accurately, in agreement with estimates by Seljak and Zaldarriaga. However, the intrinsic small scale structure of the CMB significantly degrades this power. The resulting mass constraints are useless unless one imposes a prior on the concentration parameter c. With a modest prior on c, an ambitious CMB experiment ${(0.5\mathrm{}}^{\prime }$ resolution and $1\mu \mathrm{K}$ per pixel) could determine masses of high redshift $\mathrm{}(z>\mathrm{}0.7\mathrm{}),$ large $(M>\mathrm{}5\mathrm{}\times {10}^{14}{h}^{-1}{M}_{\odot })$ clusters with $\sim 30\%$ accuracy.

• Received 13 February 2004

DOI:https://doi.org/10.1103/PhysRevD.70.023009