Weighing neutrinos with cosmic neutral hydrogen
  We investigate the signatures left by massive neutrinos on the spatial
distribution of neutral hydrogen (HI) in the post-reionization era by running
hydrodynamic simulations that include massive neutrinos as additional
collisionless particles. We find that halos in massive/massless neutrino
cosmologies host a similar amount of neutral hydrogen, although for a fixed
halo mass, on average, the HI mass increases with the sum of the neutrino
masses. Our results show that HI is more strongly clustered in cosmologies with
massive neutrinos, while its abundance, $\Omega_{\rm HI}(z)$, is lower. These
effects arise mainly from the impact of massive neutrinos on cosmology: they
suppress both the amplitude of the matter power spectrum on small scales and
the abundance of dark matter halos. Modelling the HI distribution with
hydrodynamic simulations at $z > 3$, and a simple analytic model at $z<3$, we
use the Fisher matrix formalism to conservatively forecast the constraints that
Phase 1 of the Square Kilometre Array (SKA) will place on the sum of neutrino
masses, $M_\nu\equiv \Sigma m_{\nu}$. We find that with 10,000 hours of
interferometric observations at $3 \lesssim z \lesssim 6$ from a deep and
narrow survey with SKA1-LOW, the sum of the neutrino masses can be measured
with an error $\sigma(M_\nu)\lesssim0.3$ eV (95% CL). Similar constraints can
be obtained with a wide and deep SKA1-MID survey at $z \lesssim 3$, using the
single-dish mode. By combining data from MID, LOW, and Planck, plus priors on
cosmological parameters from a Stage IV spectroscopic galaxy survey, the sum of
the neutrino masses can be determined with an error $\sigma(M_\nu)\simeq0.06$
eV (95% CL).
