Cosmological data probe massive neutrinos via their effects on the geometry of the
Universe and the growth of structure, both of which are degenerate with the late-time expansion
history. We clarify the nature of these degeneracies and the individual roles of both probes in
neutrino mass inference. Geometry is strongly sensitive to neutrino masses: within ΛCDM,
the primary cosmic microwave background anisotropies alone impose that the matter fraction
Ω
m
must increase fivefold with increasing neutrino mass. Moreover, large-scale structure
observables, like weak lensing of the CMB, are dimensionless and thus depend not on the matter
density (as often quoted) but in fact the matter fraction. We explore the consequential impact of
this distinction on the interplay between probes of structure, low-redshift distances, and CMB
anisotropies. We derive constraints on the neutrino's masses independently from their suppression
of structure and impact on geometry, showing that the latter is at least as important as the
former. While the Dark Energy Spectroscopic Instrument's recent baryon acoustic oscillation data
place stringent bounds largely deriving from their geometric incompatibility with massive
neutrinos, all recent type Ia supernova datasets drive marginal preferences for nonzero neutrino
masses because they prefer substantially larger matter fractions. Recent CMB lensing data,
however, neither exclude neutrinos' suppression of structure nor constrain it strongly enough to
discriminate between mass hierarchies. Current data thus evince not a need for modified dynamics
of neutrino perturbations or structure growth but rather an inconsistent compatibility with
massive neutrinos' impact on the expansion history. We identify two of DESI's measurements that
strongly influence its constraints, and we also discuss neutrino mass measurements in models that
alter the sound horizon.
