Cosmologists often use the full standard model of cosmology, called ΛCDM (Lambda Cold Dark Matter), to turn sky surveys into tight limits on the total mass of neutrinos. This paper asks how much those limits depend on assumptions about dark energy, the unknown cause of cosmic acceleration. The authors break down which parts of the cosmological data are sensitive to late-time expansion, and they present two different, robust ways to bound the sum of neutrino masses while relaxing dark-energy assumptions.

The question matters because different methods give very different answers today. Using the standard ΛCDM analysis of the Planck cosmic microwave background (CMB), CMB lensing, and the DESI DR2 baryon acoustic oscillation (BAO) distances gives a very tight bound, Σmν < 0.056 eV (95% confidence). That number is in mild tension with the minimum allowed sum in the “inverted” neutrino mass ordering, about 0.10 eV. By contrast, direct laboratory kinematic measurements give a much weaker bound on the electron-neutrino mass, mνe < 0.45 eV from KATRIN, which corresponds to Σmν ≲ 1.3 eV.

The first route the authors study keeps all the same cosmological data but allows the dark-energy equation of state to change. Concretely they marginalize over the common two-parameter model w(a)=w0+wa(1−a) and also test more flexible smooth histories (binned and cubic forms). They find the marginalized limit stabilizes near Σmν < 0.152 eV with current data. Adding upcoming measurements — Simons Observatory CMB lensing and a planned Spec-S5 BAO survey — would tighten the uncertainty to about σ(Σmν) ≈ 0.043 eV. The paper shows that, for smooth late-time expansions, the (w0,wa) marginalization captures the relevant uncertainty and produces a robust bound.

The second, more conservative route aims to remove any dependence on the late-time expansion history by construction. It combines the primary CMB anisotropies (marginalizing over a parameter Alens that absorbs the smoothing of acoustic peaks) with the reconstructed lensing power spectrum C_L^{κκ}. That combination isolates the neutrino effects that do not rely on assumptions about dark energy. Using current data this “late-Universe-free” approach gives a weaker bound, Σmν < 0.41 eV, which would improve to 0.31 eV with Simons Observatory data and to 0.28 eV in the ideal cosmic-variance-limited case. These bounds are looser because they trade statistical power for independence from dark-energy modeling.