Cosmology Evidence For A Normal Neutrino Hierarchy

Cosmology data increasingly favors, even under dynamical dark energy models, a normal neutrino mass hierarchy over an inverted neutrino mass hierarchy, although still not at the five sigma "discovery" level.

Constraints from direct measurements of the neutrino's absolute masses are much less constraining, although neutrino oscillation data also favors a normal neutrino mass hierarchy, in a completely independent measurement, to a similar degree.

We present cosmological parameters measurements from the full combination of DESI DR1 galaxy clustering data described with large-scale structure effective field theory. By incorporating additional datasets (photometric galaxies and CMB lensing cross-correlations) and extending the bispectrum likelihood to smaller scales using a consistent one-loop theory computation, we achieve substantial gains in constraining power relative to previous analyses. 

Combining with the latest DESI baryon acoustic oscillation data and using cosmic microwave background (CMB) priors on the power spectrum tilt and baryon density, we obtain tight constraints on the ΛCDM model, finding the Hubble constant H0=69.08±0.37 kms−1Mpc−1, the matter density fraction Ωm=0.2973±0.0050, and the mass fluctuation amplitude σ8=0.815±0.016 (or the lensing parameter S8≡σ8Ωm/0.3‾‾‾‾‾‾‾√=0.811±0.016), corresponding to 0.6%, 1.7%, and 2% precision respectively. Adding the Pantheon+ supernova sample (SNe), we find a preference of 2.6σ for the w0wa dynamical dark energy model from low-redshift data alone, which increases to 2.8σ when exchanging the SNe with Planck CMB data. 

Combining full-shape data with BAO, CMB, and SNe likelihoods, we improve the dark energy figure-of-merit by 18% and bound the sum of the neutrino masses to Mν<0.057 eV in ΛCDM and Mν<0.095 eV in the w0wa dynamical dark energy model (both at 95\% CL). 

This represents an improvement of 25% over the background expansion constraints and the strongest bound on neutrino masses in w0waCDM to date. Our results suggest that the preference for the normal ordering of neutrino mass states holds regardless of the cosmological background model, and is robust in light of tensions between cosmological datasets.

Mikhail M. Ivanov, et al., "Reanalyzing DESI DR1: 4. Percent-Level Cosmological Constraints from Combined Probes and Robust Evidence for the Normal Neutrino Mass Hierarchy" arXiv:2601.16165 (January 22, 2026).