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.