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arxiv: 2606.17994 · v1 · pith:PSPTMQCJnew · submitted 2026-06-16 · 🌌 astro-ph.CO · gr-qc· hep-ph

Constraints on the Sum of Neutrino Masses from ACT DR6 and DESI DR2 Considering Isocurvature Initial Conditions

Hongsheng Hou , Sai Wang , Zhi-Chao Zhao , Xin Zhang This is my paper

Pith reviewed 2026-06-26 23:31 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qchep-ph
keywords neutrino mass sumisocurvature perturbationscosmological constraintsACT DR6DESI DR2dark energyCMB
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The pith

Including neutrino density isocurvature modes changes the 95% upper limit on the sum of neutrino masses only from 0.052 eV to 0.057 eV in the Lambda CDM model.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines how cosmological data constrain the total mass of neutrinos when primordial fluctuations are allowed to include a neutrino density isocurvature component in addition to the usual adiabatic fluctuations. Using recent CMB observations from ACT DR6 along with DESI baryon acoustic oscillation measurements and supernova data, it finds that the upper bound on the neutrino mass sum remains nearly the same whether or not isocurvature is included. The amplitude of any isocurvature contribution is consistent with zero. The work also shows that these limits depend strongly on the assumed model for dark energy and on the choice of prior for the neutrino mass sum itself.

Core claim

Within the standard Lambda CDM cosmology the 95 percent upper limit on the sum of neutrino masses is 0.052 electronvolts assuming only adiabatic initial conditions and rises only to 0.057 electronvolts when a neutrino density isocurvature component is allowed; the isocurvature amplitude is consistent with zero. In the CPL dynamical dark energy model the corresponding limits are 0.111 and 0.115 electronvolts. The analysis uses the combination of Planck 2018, ACT DR6, SPT-3G, DESI DR2, and DES Year 5 supernova data.

What carries the argument

Joint constraints on the sum of neutrino masses and the amplitude of neutrino density isocurvature perturbations using CMB, BAO and supernova observations.

Load-bearing premise

The numerical upper limits assume either a constant dark energy equation of state or the CPL parametrization together with a flat prior on the neutrino mass sum that extends down to zero.

What would settle it

A direct laboratory measurement of the neutrino mass sum exceeding 0.057 eV while cosmological data continue to prefer the lower value, or a detection of nonzero neutrino density isocurvature amplitude in future surveys.

Figures

Figures reproduced from arXiv: 2606.17994 by Hongsheng Hou, Sai Wang, Xin Zhang, Zhi-Chao Zhao.

Figure 1
Figure 1. Figure 1: FIG. 1. Lensed CMB temperature and polarization angular power spectra assuming degenerate massive neutrinos. In the left [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The same as Fig [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. One-dimensional posterior distribution of [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. One-dimensional posterior distribution of [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Triangle plot of all cosmological parameters in the ΛCDM model. The solid lines represent the pure adiabatic initial [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Triangle plot of all cosmological parameters in the CPL model. The solid lines represent the pure adiabatic initial [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
read the original abstract

We present a robust assessment of cosmological constraints on the sum of neutrino masses ($\sum m_\nu$) when relaxing the standard assumption of purely adiabatic primordial initial conditions. Allowing for a neutrino density isocurvature (NDI) component alongside the adiabatic mode, we analyse the latest CMB-SPA combination (Planck 2018, ACT DR6, and SPT-3G), DESI DR2 baryon acoustic oscillation data, and the DES Year 5 supernova sample. Within the $\Lambda$CDM model, the 95\% upper limit weakens only marginally from $\sum m_\nu < 0.052$ eV (purely adiabatic) to $< 0.057$ eV (including NDI), with the NDI amplitude consistent with zero. In the CPL dynamical dark energy model, the adiabatic limit is $< 0.111$ eV, shifting to $< 0.115$ eV with NDI, yet the isocurvature mode remains undetected. While these limits are robust against the inclusion of isocurvature perturbations, they are highly sensitive to both the assumed dark energy equation of state and the prior lower bound on $\sum m_\nu$. Notably, the adiabatic $\Lambda$CDM limit of $0.052$ eV lies below the minimum sum required by the normal neutrino mass hierarchy ($0.05878$ eV), indicating that this bound is an artifact of the statistical prior extending to zero. Imposing a physically motivated hierarchy-informed prior raises the limit to $< 0.092$ eV. Our results demonstrate that current data show no evidence for NDI modes and that the inferred neutrino mass upper limit is robust against this extension, but a definitive, model-independent bound requires addressing prior dependencies and dark energy uncertainties. This work provides the first joint constraint on $\sum m_\nu$ and NDI using the full CMB-SPA+DESI DR2+DES dataset.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The manuscript claims that allowing neutrino density isocurvature (NDI) modes in addition to adiabatic initial conditions produces only marginal changes to the 95% upper limits on ∑m_ν derived from Planck 2018 + ACT DR6 + SPT-3G, DESI DR2 BAO, and DES Y5 supernovae. In flat ΛCDM the limit shifts from <0.052 eV (adiabatic) to <0.057 eV (with NDI); in the CPL dark-energy model the shift is from <0.111 eV to <0.115 eV, with the NDI amplitude consistent with zero in both cases. The paper explicitly notes that the numerical values remain highly sensitive to the lower bound of the ∑m_ν prior and to the dark-energy parametrization, and shows that a hierarchy-informed prior raises the adiabatic ΛCDM limit to <0.092 eV.

Significance. If the reported robustness to NDI holds, the result strengthens the reliability of current ∑m_ν upper bounds for planning next-generation surveys, because it demonstrates that isocurvature contamination does not materially alter the constraints under the same modeling assumptions. The explicit quantification of prior and dark-energy sensitivities is a positive feature that encourages cautious interpretation of the absolute scale of the limits.

minor comments (2)
  1. [Abstract and results section] The construction of the hierarchy-informed prior that yields the <0.092 eV limit should be specified (functional form, lower bound, and any truncation) so that the result can be reproduced and its effect on the NDI extension quantified.
  2. [Throughout] Notation for the NDI amplitude parameter should be made uniform between the text, tables, and any figures showing posterior contours.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our work and recommendation for minor revision. The referee's summary accurately captures the key results regarding the robustness of ∑m_ν constraints to neutrino density isocurvature modes.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper reports Bayesian posterior constraints on ∑m_ν and the NDI amplitude obtained by fitting an extended cosmological model to independent datasets (Planck+ACT+SPT CMB, DESI DR2 BAO, DES Y5 supernovae). The quoted 95% upper limits (0.052→0.057 eV in ΛCDM; 0.111→0.115 eV in CPL) are direct outputs of the likelihood analysis under identical priors and dark-energy assumptions; they are not obtained by algebraic reduction of one fitted quantity to another, nor by self-citation of a uniqueness theorem. No self-definitional, fitted-input-called-prediction, or ansatz-smuggled steps appear in the derivation chain. The manuscript itself flags the sensitivity to the ∑m_ν prior lower bound and to the dark-energy parametrization, confirming that the reported robustness statement is a comparative statement about two otherwise identical fits rather than a self-referential result.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard cosmological perturbation theory, the validity of the combined public datasets, and the chosen parametrization of isocurvature and dark energy; no new physical entities are introduced.

free parameters (3)
  • NDI amplitude
    Amplitude of the neutrino density isocurvature mode, fitted to the data and found consistent with zero.
  • ∑m_ν
    Sum of neutrino masses; the target parameter whose posterior yields the reported upper limit.
  • w0, wa (CPL model)
    Dark-energy equation-of-state parameters varied in the dynamical dark-energy extension.
axioms (2)
  • standard math Linear cosmological perturbation theory on the scales probed by CMB and BAO
    Invoked throughout the parameter estimation.
  • domain assumption Gaussian likelihood for the combined CMB, BAO, and supernova data
    Standard assumption in cosmological MCMC analyses.

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discussion (0)

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