Less isn't more: Cosmological bounds on the neutrino masses are robust to changes in the neutrino abundance

Impact Assessment

Core Contribution. This paper addresses a specific, currently active question: can a nonstandard thermal history that reduces the cosmic neutrino abundance loosen the increasingly restrictive cosmological upper bound on Σmν? The motivation is sharp — DESI DR2 combined with Planck and ACT lensing now pushes the effective neutrino mass toward zero (or negative), creating tension with the oscillation-measured lower bounds (Σmν ≥ 0.058 eV NO, ≥ 0.098 eV IO). A naive intuition is that if the CMB only infers Σmν through the neutrino energy density, then fewer neutrinos would permit heavier ones. The paper's central result — captured by the title "Less isn't more" — is that this intuition fails: reducing the neutrino abundance actually *tightens* the bound, because lowering Neff shifts the acoustic scale θs in the same direction as heavier neutrinos, and only compensating dark radiation can marginally relax the limit. This is a useful, cleanly-framed negative result that closes off one candidate resolution to the neutrino-mass tension.

Methodological Rigor. The work is methodologically solid. The authors implement a three-fluid decaying-particle model (Y → photons + dark radiation) in a modified CLASS with full perturbation equations, carefully handling tight-coupling and initialization subtleties (Table I). They fold in the correct auxiliary constraints — COBE/FIRAS spectral distortions and primordial deuterium via a modified PArThENoPE — that any physical photon-injection model must respect. The MCMC analyses span multiple dataset combinations and all three mass-ordering treatments, with explicit attention to prior-volume effects from sampling Σmν versus m₀ (Appendix B), and Pearson/partial correlation analyses to isolate physical degeneracies (Appendix A). A model-agnostic analysis varying Tν directly serves as a valuable robustness check, demonstrating that the tightness is not an artifact of the decay-specific constraints. This is a careful, well-controlled study.

Potential Impact. The impact is real but bounded. The result is a "guardrail" contribution: it tells the large community currently mining the DESI neutrino tension that thermal-history modifications reducing Neff are a dead end for relaxation, and indeed will worsen tension. The identification of a positive Σmν–Neff correlation is a physically clean and transferable insight. However, the paper is one of dozens (its own intro cites ~30 tension-resolution proposals) contributing to a crowded, fast-moving subfield. It is more likely to be cited as a useful data point than to redirect the field.

Timeliness & Relevance. Highly timely. The paper directly engages 2025 DESI DR2 results, ACT DR6, and the negative-neutrino-mass anomaly, all extremely current. The dated "September 2026" and references through 2026 place it at the frontier of this discussion.

Strengths. (1) A crisp, counterintuitive, well-explained physical result. (2) Careful statistical treatment including prior-volume and ordering subtleties often glossed over. (3) Public code releases (modified CLASS and MontePython on GitHub) and fully tabulated priors — strong reproducibility. (4) Clear pedagogical exposition of how Neff, θs, and free-streaming interplay (Figs. 1–4).

Limitations. (1) The core conclusion is a negative/robustness result — valuable but inherently limited in generative potential. (2) Scope is narrow: it rules out one class of modifications while a dozen others remain. (3) The physical mechanism (Neff effect on θs) was individually understood; the novelty is in the systematic demonstration and the marginalization over abundance, not a new principle. (4) No new data or observational capability is introduced.

Additional observations. The paper functions partly as an update/extension of the authors' prior work (Sobotka et al. 2023), adding DESI DR2 and ACT lensing, so some of its content is incremental extension of an existing pipeline. The surprising element — that a bluer ns can partially offset small-scale suppression, letting heavier neutrinos coexist with *higher* abundance — is a subtle and genuinely useful degeneracy insight. The interdisciplinary reach is confined to the cosmology/particle-astrophysics interface.

Overall, this is a rigorous, timely, clearly written contribution that provides a useful and somewhat counterintuitive constraint on the space of neutrino-tension resolutions, but is limited in transformative potential by its negative-result character and its position within a crowded subfield.