Galaxy-cluster masses via 21st-century measurements of lensing of 21-cm
  fluctuations
  We discuss the prospects to measure galaxy-cluster properties via weak
lensing of 21-cm fluctuations from the dark ages and the epoch of reionization
(EOR). We choose as a figure of merit the smallest cluster mass detectable
through such measurements. We construct the minimum-variance quadratic
estimator for the cluster mass based on lensing of 21-cm fluctuations at
multiple redshifts. We discuss the tradeoff between frequency bandwidth,
angular resolution, and number of redshift shells available for a fixed noise
level for the radio detectors. Observations of lensing of the 21-cm background
from the dark ages will be capable of detecting M>~10^12 Msun/h mass halos, but
will require futuristic experiments to overcome the contaminating sources.
Next-generation radio measurements of 21-cm fluctuations from the EOR will,
however, have the sensitivity to detect galaxy clusters with halo masses
M>~10^13 Msun/h, given enough observation time (for the relevant sky patch) and
collecting area to maximize their resolution capabilities.
