Accurately Weighing Neutrinos with Cosmological Surveys
  A promising avenue to measure the total, and potentially individual, mass of
neutrinos consists of leveraging cosmological datasets, such as the cosmic
microwave background and surveys of the large-scale structure of the universe.
In order to obtain unbiased estimates of the neutrino mass, however, many
effects ought to be included. Here we forecast, via a Markov Chain Monte Carlo
likelihood analysis, whether measurements by two galaxy surveys: DESI and {\it
Euclid}, when added to the CMB-S4 experiment, are sensitive to two effects that
can alter neutrino-mass measurements. The first is the slight difference in the
suppression of matter fluctuations that each neutrino-mass hierarchy generates,
at fixed total mass. The second is the growth-induced scale-dependent bias
(GISDB) of haloes produced by massive neutrinos. We find that near-future
surveys can distinguish hierarchies with the same total mass only at the
$1\sigma$ level; thus, while these are poised to deliver a measurement of the
sum of neutrino masses, they cannot significantly discern the mass of each
individual neutrino in the foreseeable future. We further find that neglecting
the GISDB induces up to a $1\sigma$ overestimation of the total neutrino mass,
and we show how to absorb this effect via a redshift-dependent parametrization
of the scale-independent bias.
