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Cosmological neutrino mass: a frequentist overview in light of DESI

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Taking every cosmological nuisance parameter into account by profiling, the paper finds that DESI DR2 BAO, Planck PR4, and CMB lensing together bound the summed neutrino mass to below 53 meV at 95% confidence, underneath the 59 meV floor…

desk verdict Frequentist neutrino-mass paper with a solid 53 meV limit; the headline depends on a parabolic extrapolation that deserves a dense-grid check, but the analysis is transparent and reviewable. read the letter →

arxiv 2507.12401 v2 pith:RYZTS3DD submitted 2025-07-16 astro-ph.CO

D. Chebat , C. Yèche , E. Armengaud , N. Schöneberg , M. Walther , A. de Mattia , J. Rohlf , J. Aguilar
show 46 more authors
S. Ahlen D. Bianchi D. Brooks T. Claybaugh A. Cuceu A. de la Macorra P. Doel S. Ferraro A. Font-Ribera J. E. Forero-Romero E. Gaztañaga G. Gutierrez C. Hahn H. K. Herrera-Alcantar C. Howlett D. Huterer M. Ishak J. Jimenez R. Joyce S. Juneau R. Kehoe D. Kirkby A. Kremin O. Lahav A. Lambert M. Landriau L. Le Guillou C. Magneville M. Manera R. Miquel J. Moustakas G. Niz N. Palanque-Delabrouille W. J. Percival F. Prada I. Pérez-Ràfols G. Rossi E. Sanchez D. Schlegel J. Silber D. Sprayberry G. Tarlé B. A. Weaver P. Zarrouk R. Zhou H. Zou
This is my paper
classification astro-ph.CO
keywords neutrinomasssumprofilelikelihoodFeldman-CousinsDESIBAOCMBlensingLyman-alphaforestcosmologicalparametersfrequentistinference
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper asks how tightly current cosmological data can bound the sum of neutrino masses when the analysis is done without Bayesian priors, and answers with a stricter limit than previous frequentist combinations. Using profile likelihoods and the Feldman-Cousins prescription, the authors find that the combination of DESI DR2 BAO, Planck PR4 CMB, and CMB lensing in flat $\Lambda$CDM excludes total neutrino mass above 53 meV at 95% confidence. That number sits below the 59 meV minimum allowed by normal neutrino mass ordering, so the data prefer a mass range that neutrino oscillation experiments rule out. The paper also shows that a CMB-independent combination of DESI full-shape, BBN, and eBOSS Lyman-$\alpha$ data bounds the sum at 285 meV, and that adding Lyman-$\alpha$ free-streaming information improves the constraint even though the data are not yet from DESI.

What carries the argument

The carrying object is the profile likelihood $\chi^2(\sum m_\nu)$: for each fixed total mass, all other cosmological and nuisance parameters are maximized away, and the resulting one-dimensional curve is fitted to a parabola of the form $(\sum m_\nu - \mu_0)^2/\sigma^2 - \chi^2_0$. The parameter $\sigma$ measures the constraining power of the data independently of where the minimum sits. Because nearly all $\Lambda$CDM minima fall at negative mass, the paper applies the Feldman-Cousins prescription with boundary $\mu_{\rm inf} = 0$ (and 59/100 meV for ordering-aware limits) to convert the parabola into a proper 95% C.L. upper limit. The separation of $\sigma$ from the upper limit is what allows the paper to attribute changes in the bound to either sharper data or a shifted parabola minimum.

What would settle it

Recompute the $\Lambda$CDM profile for DESI DR2 BAO + Planck PR4 + lensing on a dense grid of $\sum m_\nu$ values strictly between 0 and 0.1 eV and compare the Feldman-Cousins upper limit against the parabola extrapolation; if the $\chi^2$ curve is not parabolic near zero, the 53 meV limit shifts.

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Extended reading notes

Core claim

The central claim is that every $\Lambda$CDM profile likelihood for the summed neutrino mass $\sum m_\nu$ is truncated by the physical bound $\sum m_\nu \geq 0$: the fitted parabola reaches its minimum at a negative mass for every dataset combination considered. The most stringent upper limit, from DESI DR2 BAO + Planck PR4 + CMB lensing, is $\sum m_\nu < 53$ meV (95% C.L.) with a constraining power $\sigma = 43$ meV, a limit below the 59 meV floor of the normal ordering. Extending the model to $w_0w_a$CDM shifts the minimum into the positive region and relaxes the limit to 177 meV, while non-zero curvature relaxes it to 85 meV; only $w_0w_a$CDM shows a positive minimum. The paper further establishes that Lyman-$\alpha$ free-streaming information improves the constraining power of BAO+CMB combinations, and that the degenerate three-mass modeling used for $\sum m_\nu$ is adequate, with ordering-specific profiles for the lightest mass giving $m_l < 20$ meV (normal ordering) and 19 meV (inverted ordering) for the same strongest combination.

Load-bearing premise

The 53 meV limit assumes the profile likelihood is parabolic all the way down to the boundary: the inferred minimum lies at a negative mass for every $\Lambda$CDM combination, so the fit must be trusted outside the region where the data were actually computed.

Editorial extensions

If this is right

  • If the 53 meV limit holds, flat $\Lambda$CDM cosmology implies a neutrino mass sum below the minimum allowed by neutrino oscillations, a direct tension between the two measurements.
  • The same frequentist machinery applied to the lightest neutrino mass gives $m_l < 20$ meV (normal ordering) and $m_l < 19$ meV (inverted ordering) for DESI DR2 BAO + Planck PR4 + lensing, tightening Bayesian limits from the same data.
  • Adding eBOSS Lyman-$\alpha$ P1D to CMB+BAO improves $\sigma$ from 54 to 50/48 meV, so DESI's own Lyman-$\alpha$ data should sharpen the bound further.
  • The CMB-independent combination of DESI DR1 full-shape + BBN + Lyman-$\alpha$ reaches $\sum m_\nu \leq 285$ meV, showing that large-scale-structure data alone can constrain neutrino mass.
  • In $w_0w_a$CDM the profile minimum becomes positive and the upper limit rises to 177 meV, so model extensions decide whether the neutrino mass sits above or below the ordering floor.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A dense sampling of the profile near $\sum m_\nu = 0$ would be a cheap test of whether the 53 meV limit is real or a parabolic artifact, since the paper's fit was made from points in the positive-mass region while the minimum sits in the unphysical sector.
  • If upcoming DESI Lyman-$\alpha$ and full-shape data sharpen $\sigma$ toward the forecast 20-30 meV range, the profile-plus-Feldman-Cousins approach could become the standard way to report neutrino limits because it separates constraining power from boundary effects.
  • The apparent preference for negative mass tracks the dark-energy model: only $w_0w_a$CDM shows a positive minimum, suggesting the 'negative mass' preference may be a symptom of the cosmological model rather than a measurement of neutrino physics.
  • The same boundary-aware frequentist treatment could be applied to other cosmological parameters with physical boundaries, such as curvature or the dark-energy equation of state, where Bayesian volume effects are a concern.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper derives frequentist constraints on the cosmological neutrino mass sum Σmν using profile likelihoods and the Feldman–Cousins prescription. It combines DESI DR1/DR2 BAO, DESI DR1 full-shape, Planck PR3/PR4 and ACT CMB, CMB lensing, BBN, supernovae, and eBOSS Lyman-α P1D likelihoods, mostly within flat ΛCDM and some extensions. The headline result is a 95% C.L. upper limit Σmν < 53 meV from DESI DR2 BAO + Planck PR4 + CMB lensing, which lies below the 59 meV normal-ordering floor; a CMB-independent combination (DESI DR1 full-shape + BBN + eBOSS Lyman-α) gives Σmν ≤ 285 meV. The paper also translates the constraints to the lightest neutrino mass ml, obtaining 20 and 19 meV 95% limits for normal and inverted ordering for the most constraining combination.

Significance. If correct, the sub-59 meV limit is a striking result, as it would exclude the normal neutrino mass ordering at 95% C.L. and thereby challenge the standard three-flavor mass spectrum when combined with oscillation data. The frequentist approach avoids prior-volume effects that can affect Bayesian analyses, and the use of public likelihoods plus a Zenodo data release makes the analysis reproducible. The decomposition of the constraint into the profile minimum μ0 and constraining power σ is a useful tool for comparing datasets. However, the central claim rests on the parabolic extrapolation of profiles whose minima are in the unphysical negative-mass region, and on the Feldman–Cousins construction, so the exact numerical limits should be treated with corresponding caution.

major comments (3)
  1. [Section 2.2, Eq. (2.2)] The second branch of the piecewise definition of R(x, µ) is algebraically incorrect. For x < µinf, µbest = µinf, so the denominator should be P(x|µinf) = exp[−(x−µinf)^2/2]. The expression written, exp[−(µinf−µ)^2/2], is independent of the observed x and is not the likelihood ratio used by Feldman–Cousins. Please correct this equation and verify that the numerical FC limits in Tables 2, 3, and 5 are computed with the correct ratio.
  2. [Section 4.1.1 and Table 2] The headline limit Σmν < 53 meV is obtained by applying the FC prescription to a parabolic fit with (μ0, σ) = (−36, 43) meV; the parabola minimum lies roughly 40 meV below the lowest mass at which the profile was evaluated. Because the profile is cut by the Σmν ≥ 0 bound, the limit depends on the assumed quadratic shape in a region with no explicit computations. The paper does not report the number of profile points, their spacing, or the fit residuals. Please provide a dense profile evaluation near zero (e.g., 5 meV steps from 0 to 100 meV), report the goodness of fit, and show how the FC upper limit changes if the empirical profile is used directly rather than the fitted parabola.
  3. [Section 4.2 and Tables 2, 3, 5] The text notes that 'the parabolic fit is worse in w0waCDM', but no goodness-of-fit statistic is reported for any of the parabolic fits, including the ΛCDM fits behind the central claim. Please add a fit-quality indicator (e.g., the χ² of the parabola relative to the profile points or the maximum residual) for all models in Tables 2, 3, and 5, and discuss the sensitivity of the reported μ95 values to the fit range and to the arbitrary 0.005 eV reference in Eq. (2.1).
minor comments (5)
  1. [Abstract and throughout] The expression 'P mν' appears in many places where 'Σmν' is clearly intended (e.g., the abstract, Eq. (1.1), and later sections); please correct these to avoid confusion.
  2. [Section 2.1] The choice of 0.005 eV as the reference mass in Eq. (2.1) is described as arbitrary; a brief comment or test showing the insensitivity of the derived limits to this choice would improve the presentation.
  3. [Section 3.1] The sentence 'In the following, we detail data, data products and codes used in our analysis as well as the corresponding nomenclature for the article' is redundant and could be simplified.
  4. [Table 1] The label 'T able 1' contains a spacing typo and should read 'Table 1'.
  5. [Section 6.2] The abstract reports limits of '20 and 19 meV', while Eqs. (6.2)–(6.3) use the '<' symbol; please make the notation consistent throughout.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: all constraints derive from external data via profile likelihoods and Feldman-Cousins intervals.

full rationale

The paper's derivation chain is self-contained with respect to the neutrino mass inference. The profile likelihoods are constructed by maximizing the full likelihood over nuisance parameters for fixed Σmν, using external datasets (DESI BAO/FS, Planck PR3/PR4, ACT DR6, eBOSS Lyman-α P1D, BBN). The parabolic fits in Eq. (2.1) and Table 2 are summary fits to the computed profile points; the reported 95% C.L. limits (e.g., 53 meV) are obtained by the Feldman-Cousins prescription applied to those fitted profiles, not by fitting to the final limit. Citations to works with overlapping authorship (e.g., Walther et al. 2025 for the Lyssa likelihood, Schöneberg 2024 for BBN) provide externally grounded data products and simulation-based likelihoods based on SDSS/eBOSS data and independent hydrodynamical simulations; they are independent support rather than load-bearing self-citations. The paper explicitly flags where the parabolic approximation is less reliable (Section 4.2: 'the parabolic fit is worse in w0waCDM'; Section 6.1: 'the analysis would be limited to a region where the parabolic fit cannot be expected to hold up'), which is a statistical robustness concern, not a circularity. No equation or fitted parameter is renamed as a prediction, and no uniqueness claim is imported from the authors' prior work.

Assumptions & free parameters 11 free parameters · 9 assumptions · 0 invented entities

The analysis is an inference pipeline built on a long chain of external assumptions: the LambdaCDM model, oscillation-measured mass splittings, CMB and LSS likelihoods, Lyman-alpha emulators, and the quadratic-profile statistical model. No new physical entities are introduced; the free parameters are the usual cosmological and nuisance parameters of the input likelihoods.

free parameters (11)
  • Omega_m (matter density fraction) = fitted, profile-dependent
    Central parameter for the geometrical neutrino-mass effect; constrained jointly by DESI BAO and CMB data (Section 1, Eq. 1.2).
  • H0 (Hubble constant) = fitted, profile-dependent
    Degenerate with Omega_m in the geometrical effect; enters Eq. (1.2).
  • ln(10^10 A_s) (primordial amplitude) = fitted, profile-dependent
    Amplitude of primordial scalar fluctuations; used in CMB and Lyman-alpha likelihoods (Section 3.1).
  • n_s (spectral index) = fitted, profile-dependent
    Spectral tilt; drives the comparison between Planck compressed constraints and Lyman-alpha P1D (Sections 5.1 and 5.2).
  • Omega_b h^2 (baryon density) = 0.02218 +/- 0.00055 in BBN prior
    BBN constraint from Schoneberg 2024 used in Section 5; also fitted by CMB likelihoods.
  • tau (reionization optical depth) = fitted, frozen in Section 5 combinations
    CMB nuisance parameter; frozen when the likelihood has no sensitivity to it (Section 3.2).
  • w0 and wa (dark energy equation of state) = fitted in w0waCDM extension
    CPL parameters that relax the neutrino mass constraint in Section 4.2.
  • Omega_K (curvature) = fitted in non-flat extension
    Curvature degenerates with the neutrino mass through the geometrical effect (Section 4.2).
  • nLya and ALya (Lyman-alpha P1D nuisance parameters) = fitted via Taylor/Lyssa emulators
    Parameters of the Lyman-alpha forest P1D model used for the CMB-independent constraint (Section 5.2).
  • DESI full-shape nuisance parameters (bias, counterterms, etc.) = many, fitted
    Internal parameters of the DESI DR1 full-shape likelihood (Section 3.1).
  • CMB likelihood nuisance parameters (foregrounds, calibration, etc.) = many, fitted
    Nuisance parameters in the Planck and ACT likelihoods; not individually reported in this paper.
assumptions (9)
  • domain assumption Three neutrino mass eigenstates with oscillation-measured squared-mass differences (PDG 2024); NO floor 58.98 meV, IO floor 99.82 meV
    Used for Eq. (1.1) and as lower boundaries mu_inf = 59 and 100 meV in the Feldman-Cousins limits of Section 2.2; external input, not derived in this paper.
  • domain assumption Flat LambdaCDM with three degenerate massive neutrinos (m1 = m2 = m3 = Σmν/3, Eq. 6.1) is the baseline model
    Baseline for all Section 4 and 5 profiles; the degenerate assumption is standard and is checked for only one data combination in Section 6.1.
  • domain assumption Spatial flatness (ΩK = 0) for baseline LambdaCDM
    Assumed in Sections 4.1 and 5; relaxed only in the curvature extension of Section 4.2.
  • domain assumption Dark energy is a cosmological constant in baseline, or CPL parametrization w(z) = w0 + (z/(1+z)) wa in extension
    Defines the w0waCDM extension in Section 4.2.
  • standard math Profile likelihood of a Gaussian likelihood is a parabola: Δχ2 = (x - mu0)^2 / sigma^2 (Eq. 2.1)
    The parabolic fit is the basis for sigma and for the Feldman-Cousins upper limits; the paper notes the fit is worse in w0waCDM (Section 4.2).
  • standard math Feldman-Cousins ordering with a Gaussian likelihood and a lower boundary mu_inf produces valid confidence intervals
    Adapted in Section 2.2 to compute mu95, mu95(NO), and mu95(IO).
  • domain assumption The Taylor and Lyssa Lyman-alpha P1D emulators correctly map (nLya, ALya) to the observed eBOSS P1D over the explored parameter space
    Used for the CMB-independent constraint in Section 5.2; both emulators are simulation-based and share authors with this paper.
  • domain assumption Compressed Planck constraints on n_s and ln(10^10 A_s) are sufficient proxies for the full CMB likelihood in Section 5.1
    The authors intentionally discard geometric CMB information to isolate free-streaming constraints from large-scale structure.
  • standard math CAMB Boltzmann solver correctly computes CMB and matter power spectra for the fitted parameters
    All profiles use CAMB (Section 3.2); the solver is a standard external tool rather than new physics.

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Cite this review

Pith. "Pith review of Cosmological neutrino mass: a frequentist overview in light of DESI." pith.science (2026). https://pith.science/paper/RYZTS3DD

@misc{pith2026250712401,
  author       = {Pith},
  title        = {Pith review of: Cosmological neutrino mass: a frequentist overview in light of DESI},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RYZTS3DD}},
  note         = {Machine review of arXiv:2507.12401}
}
abstract

We derive constraints on the neutrino mass using a variety of recent cosmological datasets, including DESI BAO, the full-shape analysis of the DESI matter power spectrum and the one-dimensional power spectrum of the Lyman-$\alpha$ forest (P1D) from eBOSS quasars as well as the cosmic microwave background (CMB). The constraints are obtained in the frequentist formalism by constructing profile likelihoods and applying the Feldman-Cousins prescription to compute confidence intervals. This method avoids potential prior and volume effects that may arise in a comparable Bayesian analysis. Parabolic fits to the profiles allow one to distinguish changes in the upper limits from variations in the constraining power $\sigma$ of the different data combinations. We find that all profiles in the $\Lambda$CDM model are cut off by the $\sum m_\nu \geq 0$ bound, meaning that the corresponding parabolas reach their minimum in the unphysical sector. The most stringent 95% C.L. upper limit is obtained by the combination of DESI DR2 BAO, Planck PR4 and CMB lensing at 53 meV, below the minimum of 59 meV set by the normal ordering. Extending $\Lambda$CDM to non-zero curvature and $w_0w_\mathrm{a}$CDM relaxes the constraints past 59 meV again, but only $w_0w_\mathrm{a}$CDM exhibits profiles with a minimum at a positive value. Using a combination of DESI DR1 full-shape, BBN and eBOSS Lyman-$\alpha$ P1D, we successfully constrain the neutrino mass independently of the CMB. This combination yields $\sum m_\nu \leq 285$ meV (95% C.L.). The addition of DESI full-shape or Lyman-$\alpha$ P1D to CMB and DESI BAO results in small but noticeable improvement of the constraining power of the data. Lyman-$\alpha$ free-streaming measurements especially improve the constraint. Since they are based on eBOSS data, this sets a promising precedent for upcoming DESI data.

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Forward citations

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