Observing the Epoch of Reionization with the Cosmic Microwave Background
  We review the observable consequences of the epoch of reionization (EoR) on
the cosmic microwave background (CMB), and the resulting constraints on the
EoR. We discuss how Thomson scattering with the free electrons produced during
EoR equates to an optical depth for CMB photons. The optical depth measurements
from the WMAP and Planck satellites, using large-scale CMB polarization power
spectra, is one of the few current constraints on the timing of cosmic
reionization. We also present forecasts for the precision with which the
optical depth will be measured by future satellite missions. Second, we
consider the kinematic Sunyaev-Zel'dovich (kSZ) effect, and how the kSZ power
spectrum depends on the duration of reionization. We review current
measurements of the kSZ power and forecasts for future experiments. Finally, we
mention proposals to look for spectral distortions in the CMB that are related
to the electron temperature at EoR, and ideas to map the variations in the
optical depth across the sky.
