Decisive Cosmological Evidence for the Normal Neutrino Mass Hierarchy from DESI Data Release 2

Abstract: The determination of the neutrino mass hierarchy—whether Normal (NH) or Inverted (IH)—is a fundamental challenge in physics, with profound implications for cosmology and searches for neutrinoless double-beta decay. We address this question by computing the Bayesian evidence for each hierarchy, combining cosmological constraints on the sum of neutrino masses () from the Dark Energy Spectroscopic Instrument (DESI) Data Release 2 with the latest neutrino oscillation data from NuFIT 6.0. To ensure the robustness of our conclusions against prior assumptions, we perform the analysis using two distinct frameworks: a physically-motivated hierarchical (SJPV) prior and an objective, information-theoretic (HS) reference prior. Within the standard CDM cosmological model, the DESI DR2 data, which constrains eV (95% C.L.), places the minimum allowed mass for the IH ( eV) in severe tension with observations. This results in decisive evidence for the Normal Hierarchy, with a Bayes factor () of even under the most conservative (HS) prior. We test the sensitivity of this conclusion to the cosmological model by extending the analysis to a CDM parameterization, finding that the preference, while reduced, remains strong (). The decisive preference for the NH implies a significantly more challenging landscape for upcoming neutrinoless double-beta decay experiments, as our posterior for the effective Majorana mass () is suppressed into the few-meV range, well below the predictions for the now-disfavored Inverted Hierarchy.