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

Abstract: We present a novel approach to derive constraints on neutrino masses from cosmological data, while taking into account our ignorance of the neutrino mass ordering. We derive constraints from a combination of current and future cosmological datasets on the total neutrino mass $M_\nu$ and on the mass fractions carried by each of the mass eigenstates, after marginalizing over the (unknown) neutrino mass ordering, either normal (NH) or inverted (IH). The bounds take therefore into account the uncertainty related to our ignorance of the mass hierarchy. This novel approach is carried out in the framework of Bayesian analysis of a typical hierarchical problem. In this context, the choice of the neutrino mass ordering is modeled via the discrete hyperparameter $h_{type}$. The preference for either the NH or the IH scenarios is then encoded in the posterior distribution of $h_{type}$ itself. Current CMB measurements assign equal odds to the two hierarchies, and are thus unable to distinguish between them. However, after the addition of BAO measurements, a weak preference for NH appears, with odds of 4:3 from Planck temperature and large-scale polarization in combination with BAO (3:2 if small-scale polarization is also included). Forecasts suggest that the combination of upcoming CMB (COrE) and BAO surveys (DESI) may determine the neutrino mass hierarchy at a high statistical significance if the mass is very close to the minimal value allowed by oscillations, as for NH and $M_\nu=0.06$ eV there is a 9:1 preference of NH vs IH. On the contrary, if $M_\nu$ is of the order of 0.1 eV or larger, even future cosmological observations will be inconclusive. The unbiased limit on $M_\nu$ we obtain with this innovative statistical strategy is crucial for ongoing and planned neutrinoless double beta decay searches.