Revisiting the impact of neutrino mass hierarchies on neutrino mass constraints in light of recent DESI data

Recent results from DESI combined with cosmic microwave background data give the tightest constraints on the sum of neutrino masses to date. However, these analyses approximate the neutrino mass hierarchy by three degenerate-mass (DM) neutrinos, instead of the normal (NH) and inverted hierarchies (IH) informed by terrestrial neutrino oscillation experiments. Given the stringency of the upper limits from DESI data, we test explicitly whether the inferred neutrino constraints are robust to the choice of neutrino mass ordering using both Bayesian and frequentist methods. For Planck data alone, we find that the DM hierarchy presents a good approximation to the physically motivated hierarchies while showing a strong dependence on the assumed lower bound of the prior, confirming previous studies. For the combined Planck and DESI baryon acoustic oscillation data, we find that assuming NH ($M_\mathrm{tot} < 0.13\,\mathrm{eV}$) or IH ($M_\mathrm{tot} < 0.16\,\mathrm{eV}$) loosens the Bayesian upper limits compared to the DM approximation ($M_\mathrm{tot} < 0.086\,\mathrm{eV}$). The frequentist analysis shows that the different neutrino models fit the data equally well and the loosening of the constraints can thus be attributed to the lower bounds induced by NH and IH. Overall, we find that the DM hierarchy presents a good approximation to the physically motivated hierarchies also for Planck+DESI data as long as the corresponding lower neutrino mass bounds are imposed.