Towards a cosmological neutrino mass detection
  Future cosmological measurements should enable the sum of neutrino masses to
be determined indirectly through their effects on the expansion rate of the
Universe and the clustering of matter. We consider prospects for the
gravitationally lensed Cosmic Microwave Background anisotropies and Baryon
Acoustic Oscillations in the galaxy distribution, examining how the projected
uncertainty of $\approx15$ meV on the neutrino mass sum (a 4$\sigma$ detection
of the minimal mass) might be reached over the next decade. The current
1$\sigma$ uncertainty of $\approx 103$ meV (Planck-2015+BAO-15) will be
improved by upcoming 'Stage-3' CMB experiments (S3+BAO-15: 44 meV), then
upcoming BAO measurements (S3+DESI: 22 meV), and planned next-generation 'Stage
4' CMB experiments (S4+DESI: 15-19 meV, depending on angular range). An
improved optical depth measurement is important: the projected neutrino mass
uncertainty increases to $26$ meV if S4 is limited to $\ell>20$ and combined
with current large-scale polarization data. Looking beyond $\Lambda$CDM,
including curvature uncertainty increases the forecast mass error by $\approx$
50% for S4+DESI, and more than doubles the error with a two-parameter dark
energy equation of state. Complementary low-redshift probes including galaxy
lensing will play a role in distinguishing between massive neutrinos and a
departure from a $w=-1$, flat geometry.
