  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.
