Towards Neutrino Mass from Cosmology without Optical Depth Information
  With low redshift probes reaching unprecedented precision, uncertainty of the
CMB optical depth is expected to be the limiting factor for future cosmological
neutrino mass constraints. In this paper, we discuss to what extent
combinations of CMB lensing and galaxy surveys measurements at low redshifts
$z\sim 0.5-5$ will be able to make competitive neutrino mass measurements
without relying on any optical depth constraints. We find that the combination
of LSST galaxies and CMB-S4 lensing should be able to achieve constraints on
the neutrino mass sum of 25meV without optical depth information, an
independent measurement that is competitive with or slightly better than the
constraint of 30meV possible with CMB-S4 and present-day optical depth
measurements. These constraints originate both in structure growth probed by
cross-correlation tomography over a wide redshift range as well as, most
importantly, the shape of the galaxy power spectrum measured over a large
volume. We caution that possible complications such as higher-order biasing and
systematic errors in the analysis of high redshift galaxy clustering are only
briefly discussed and may be non-negligible. Nevertheless, our results show
that new kinds of high-precision neutrino mass measurements at and beyond the
present-day optical depth limit may be possible.
