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 (CMB) anisotropies and baryon acoustic oscillations (BAOs) in the galaxy distribution, examining how the projected uncertainty of $\ensuremath{\approx}15\text{ }\text{ }\mathrm{meV}$ on the neutrino mass sum (a $4\ensuremath{\sigma}$ detection of the minimal mass) might be reached over the next decade. The current $1\ensuremath{\sigma}$ uncertainty of $\ensuremath{\approx}103\text{ }\text{ }\mathrm{meV}$ ($\text{Planck}\text{\ensuremath{-}}2015+\mathrm{BAO}\text{\ensuremath{-}}15$) will be improved by upcoming ``Stage-3'' (S3) CMB experiments ($\mathrm{S}3+\mathrm{BAO}\text{\ensuremath{-}}15:\text{ }44\text{ }\text{ }\mathrm{meV}$), then upcoming BAO measurements ($\mathrm{S}3+\mathrm{DESI}:\text{ }22\text{ }\text{ }\mathrm{meV}$), and planned next-generation ``Stage 4'' (S4) CMB experiments ($\mathrm{S}4+\mathrm{DESI}:\text{ }15\char21{}19\text{ }\text{ }\mathrm{meV}$, 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 $\ensuremath{\ell}g20$ and combined with current large-scale polarization data. Looking beyond $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$, including curvature uncertainty increases the forecast mass error by $\ensuremath{\approx}50%$ for $\mathrm{S}4+\mathrm{DESI}$, 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 $w=\ensuremath{-}1$, flat geometry.