Neutrino masses and beyond-$\Lambda$CDM cosmology with LSST and future
  CMB experiments
  Cosmological measurements over the next decade will enable us to shed light
on the content and evolution of the Universe. Complementary measurements of the
Cosmic Microwave Background (CMB) and Baryon Acoustic Oscillations are expected
to allow an indirect determination of the sum of neutrino masses, within the
framework of the flat $\Lambda$CDM model. However, possible deviations from
$\Lambda$CDM such as a non-zero cosmological curvature or a dark energy
equation of state with $w\neq -1$ would leave similar imprints on the expansion
rate of the Universe and clustering of matter. We show how future CMB
measurements can be combined with late-time measurements of galaxy clustering
and cosmic shear from the Large Synoptic Survey Telescope to alleviate this
degeneracy. Together, they are projected to reduce the uncertainty on the
neutrino mass sum to 30 meV within this more general cosmological model.
Achieving a 3$\sigma$ measurement of the minimal 60 meV mass (or 4$\sigma$
assuming $w=-1$) will require a five-fold improved measurement of the optical
depth to reionization, obtainable through a large-scale CMB polarization
measurement.
