Neutrino Masses, Dark Energy and the Gravitational Lensing of
  Pregalactic HI
  We study the constraints which the next generation of radio telescopes could
place on the mass and number of neutrino species by studying the gravitational
lensing of high redshift 21 cm emission in combination with wide-angle surveys
of galaxy lensing. We use simple characterizations of reionization history and
of proposed telescope designs to forecast the constraints and detectability
threshold for neutrinos. It is found that the degeneracy between neutrino
parameters and dark energy parameters is significantly reduced by incorporating
21 cm lensing. The combination of galaxy and 21 cm lensing could constrain the
sum of the neutrino masses to within ~ 0.04 eV and the number of species to
within ~ 0.1. This is an improvement of a factor of 2.6 in mass and 1.3 in
number over a galaxy lensing survey alone. This includes marginalizing over an
11 parameter cosmological model with a two parameter model for the dark energy
equation of state. If the dark energy equation of state is held fixed at w =
p/\rho=-1 the constraints improve to ~0.03 eV and 0.04. These forecasted errors
depend critically on the fraction of sky that can be surveyed in redshifted 21
cm emission (25% is assumed here) and the redshift of reionization ($z=7$ is
assumed here). It is also found that neutrinos with masses too small to be
detected in the data could none the less cause a significant bias in the
measured dark energy equation of state.
