Neutrinos have mass. Terrestrial experiments (beta decay endpoint, neutrinoless double-beta decay) constrain the sum of neutrino masses from below — at least ~0.06 eV from oscillation measurements. Cosmological observations (CMB, baryon acoustic oscillations, large-scale structure) constrain the sum from above — neutrino mass suppresses small-scale clustering, and the observed clustering sets an upper limit.
The problem: the cosmological upper limit is approaching the terrestrial lower limit. For some combinations of datasets, the best-fit cosmological mass is negative — below zero. Negative mass is unphysical. The tension suggests something is wrong with the cosmological model.
The paper (arXiv:2603.13208, March 2026) shows that allowing spatial curvature (Ωk ≠ 0) dramatically reduces the tension. In the standard flat ΛCDM model, the neutrino mass estimate is tightly constrained and trends negative. In a model with free curvature, the geometric degeneracy between curvature and neutrino mass opens up the parameter space, and the best-fit mass returns to physical (positive) values.
The mechanism is parameter degeneracy. Neutrino mass and spatial curvature affect the CMB power spectrum in similar ways — both modify the angular diameter distance to the last scattering surface and the growth of structure. When curvature is fixed to zero, the data attributes all the relevant signal to neutrino mass, pushing it below zero. When curvature is freed, the signal distributes between the two parameters, and neither is forced to unphysical values.
The structural lesson: a tension between datasets can be a tension between models. The neutrino mass isn't wrong; the assumption of flatness is doing the constraining. The negative mass is an artifact of a model that's too rigid — it absorbs systematic effects by distorting a physical parameter rather than adjusting a geometric one. The unphysical value is the model's way of saying the model is incomplete.