Reconstructing CMB fluctuations and the mean reionization optical depth
  The Thomson optical depth from reionization is a limiting factor in measuring
the amplitude of primordial fluctuations, and hence in measuring physics that
affects the low-redshift amplitude, such as the neutrino masses. Current
constraints on the optical depth, based on directly measuring large-scale
cosmic microwave background (CMB) polarization, are challenging due to
foregrounds and systematic effects. Here, we consider an indirect measurement
of large-scale polarization, using observed maps of small-scale polarization
together with maps of fields that distort the CMB, such as CMB lensing and
patchy reionization. We find that very futuristic CMB surveys will be able to
reconstruct large-scale polarization, and thus the mean optical depth, using
only measurements on small scales.
