Can cosmology detect hierarchical neutrino masses?

We have carefully analyzed the potential of future cosmic microwave background (CMB) and large scale structure (LSS) measurements to probe neutrino masses. We perform a Fisher matrix analysis on a nine-dimensional cosmological parameter space and find that data from the Planck CMB experiment combined with the Sloan Digital Sky Survey (SDSS) can measure a value for the sum of all three active neutrino mass eigenstates of 0.12 eV at 95% C.L. This is almost at the level of the 0.06 eV mass suggested by current neutrino oscillation data. A future galaxy survey with an order of magnitude larger survey volume than the SDSS would allow for a neutrino mass determination of 0.03-0.05 eV (95% C.L.).