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We present a novel approach to derive constraints on neutrino masses fromcosmological data, while taking into account our ignorance of the neutrino massordering. We derive constraints from a combination of current and futurecosmological datasets on the total neutrino mass $M_\nu$ and on the massfractions carried by each of the mass eigenstates, after marginalizing over the(unknown) neutrino mass ordering, either normal (NH) or inverted (IH). Thebounds take therefore into account the uncertainty related to our ignorance ofthe mass hierarchy. This novel approach is carried out in the framework ofBayesian analysis of a typical hierarchical problem. In this context, thechoice of the neutrino mass ordering is modeled via the discrete hyperparameter$h_{type}$. The preference for either the NH or the IH scenarios is thenencoded in the posterior distribution of $h_{type}$ itself. Current CMBmeasurements assign equal odds to the two hierarchies, and are thus unable todistinguish between them. However, after the addition of BAO measurements, aweak preference for NH appears, with odds of 4:3 from Planck temperature andlarge-scale polarization in combination with BAO (3:2 if small-scalepolarization is also included). Forecasts suggest that the combination ofupcoming CMB (COrE) and BAO surveys (DESI) may determine the neutrino masshierarchy at a high statistical significance if the mass is very close to theminimal value allowed by oscillations, as for NH and $M_\nu=0.06$ eV there is a9:1 preference of NH vs IH. On the contrary, if $M_\nu$ is of the order of 0.1eV or larger, even future cosmological observations will be inconclusive. Theunbiased limit on $M_\nu$ we obtain with this innovative statistical strategyis crucial for ongoing and planned neutrinoless double beta decay searches.

physics letters b

A novel approach to quantifying the sensitivity of current and future  cosmological datasets to the neutrino mass ordering through Bayesian  hierarchical modeling