Abstract
Recent works combining neutrino oscillation and cosmological data to
determine the neutrino hierarchy found a range of odds in favour of the normal
hierarchy. These results arise from differing approaches to incorporating prior
knowledge about neutrinos. We develop a hierarchy-agnostic prior and show that
the hierarchy cannot be conclusively determined with current data. The
determination of the hierarchy is limited by the neutrino mass scale
$\Sigma_\nu$ measurement. We obtain a target precision of
$\sigma(\Sigma_\nu) = 0.014$ eV for conclusively establishing the normal
hierarchy with future data.
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