What will it take to measure individual neutrino mass states using cosmology?

We study the impact of assumptions made about the neutrino mass ordering on cosmological parameter estimation with the purpose of understanding whether in the future it will be possible to infer the specific neutrino mass distribution from cosmological data. We find that although the commonly used assumption of a degenerate neutrino hierarchy is manifestly wrong and leads to changes in cosmological observables such as the cosmic microwave background and large scale structure compared to the correct (normal or inverted) neutrino hierarchy, the induced changes are so small that even with extremely optimistic assumptions about future data they will remain undetectable. We are thus able to conclude that while cosmology can probe the neutrino contribution to the cosmic energy density extremely precisely (and hence provide a detection of a non-zero total neutrino mass at high significance), it will not be possible to directly measure the individual neutrino masses.