Title: Strong Bayesian Evidence for the Normal Neutrino Hierarchy,
Abstract: The configuration of the three neutrino masses can take two forms, known as
the normal and inverted hierarchies. We compute the Bayesian evidence
associated with these two hierarchies. Previous studies found a mild preference
for the normal hierarchy, and this was driven by the asymmetric manner in which
cosmological data has confined the available parameter space. Here we identify
the presence of a second asymmetry, which is imposed by data from neutrino
oscillations. By combining constraints on the squared-mass splittings with the
limit on the sum of neutrino masses of $\Sigma m_\nu < 0.13$ eV, and using a
minimally informative prior on the masses, we infer odds of 42:1 in favour of
the normal hierarchy, which is classified as "strong" in the Jeffreys' scale.
We explore how these odds may evolve in light of higher precision cosmological
data, and discuss the implications of this finding with regards to the nature
of neutrinos. Finally the individual masses are inferred to be $m_1 =
3.80^{+26.2}_{-3.73} \, \text{meV}, m_2 = 8.8^{+18}_{-1.2} \, \text{meV}, m_3 =
50.4^{+5.8}_{-1.2} \, \text{meV}$ ($95\%$ credible intervals).