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Neutrino masses from large-scale structures: future sensitivity and theory dependence

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Galaxy surveys plus CMB can weigh neutrinos to 7 meV, forecasts show.

desk verdict A careful, honest Fisher forecast that puts real numbers on the one-loop bispectrum's value for neutrino mass, but the headline 7 meV sensitivity should be treated as optimistic given the acknowledged ~50% systematics and unvalidated high-redshift extrapolation. read the letter →

arxiv 2412.04959 v2 pith:IOUPZS3B submitted 2024-12-06 astro-ph.CO gr-qchep-ph

Davide Racco , Pierre Zhang , Henry Zheng This is my paper · ORCID
classification astro-ph.COgr-qchep-ph MSC 83F0585A40
keywords sumofneutrinomassesEFTofLSSone-loopbispectrumFisherforecastDESIMegaMapperCMBnewphysics
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 forecasts how precisely upcoming cosmological surveys can measure the sum of neutrino masses, Σmν, using effective field theory predictions for galaxy clustering at one loop. It finds that Planck combined with DESI should reach a 1σ sensitivity of 15 meV, while a Stage-4 CMB experiment combined with the proposed MegaMapper survey could reach 7 meV, with the one-loop bispectrum contributing roughly 10% and 30% of the constraining power, respectively. The authors also test how these sensitivities change when the model is extended with new physics—extra relativistic species, neutrino self-interactions, spatial curvature, or a varying electron mass—and find that for S4+MegaMapper a 1σ shift in any of these parameters displaces the inferred Σmν by only O(1) meV. A measurement this precise would complement laboratory neutrino experiments and could discriminate the neutrino mass ordering.

What carries the argument

The analysis is built on the Effective Field Theory of Large-Scale Structure (EFTofLSS) at one loop: the galaxy power spectrum monopole and quadrupole and the galaxy bispectrum monopole in redshift space, with bias expansion and counterterms, evaluated with fast loop-integral code, and Fisher matrices for LSS surveys combined with CMB likelihood chains. Neutrino effects enter through the fν corrections—the power spectrum is suppressed by roughly (1−8fν) and the bispectrum by (1−16fν) on scales k≫kFS—so redshift-space distortions help break the degeneracy with galaxy bias. EFT parameters are taken from BOSS best fits and extrapolated in redshift, and the theory reach kmax is set by requiring the estimated two-loop error to stay below the survey data error.

What would settle it

Compare the one-loop EFTofLSS power spectrum and bispectrum predictions against N-body simulations with massive neutrinos at z≈2–5 on scales up to the adopted kmax values; if the residuals systematically exceed the survey data errors at k≳0.3 h/Mpc, the projected sensitivities, especially the 7 meV for S4+MegaMapper, would be overestimated. Alternatively, run the same Fisher pipeline on BOSS data and compare the forecast error bars to the actual measured ones to calibrate the roughly 50% systematic from covariance and window approximations.

Watch

Extended reading notes

Core claim

The central claim is that with the state-of-the-art EFTofLSS, including the one-loop power spectrum and bispectrum, the projected 1σ uncertainty on the sum of neutrino masses is σ(Σmν)=15 meV for Planck+DESI and 7 meV for S4+MegaMapper, assuming normal ordering and a fiducial Σmν=60 meV. The one-loop bispectrum contributes about 10% and 30% of these constraints respectively, and in the S4+MegaMapper combination the shift in Σmν induced by a 1σ shift of new physics parameters (extra relativistic species, neutrino self-interactions, curvature, electron-mass variation) is suppressed to about 1–4 meV, making the measurement robust against those extensions. The robustness comes from the complementarity of CMB and LSS probes breaking parameter degeneracies.

Load-bearing premise

The forecasts assume the one-loop EFTofLSS predictions, especially the bispectrum, remain accurate out to the adopted maximum wavenumbers (kmax up to about 0.76 h/Mpc for MegaMapper at z=4.3), with EFT parameters extrapolated from BOSS by a redshift-scaling prescription; if the one-loop model breaks down on those scales, the projected 7 meV sensitivity would be optimistic.

Editorial extensions

If this is right

  • Within about five years, Planck+DESI could reach σ(Σmν)=15 meV, giving a roughly 4σ detection of a non-zero sum and more than 2σ discrimination between normal and inverted ordering for the minimal normal-ordering mass.
  • With S4+MegaMapper, σ(Σmν)=7 meV would make the mass ordering accessible at about 5σ, a regime where cosmological precision rivals laboratory experiments.
  • The one-loop bispectrum sharpens the MegaMapper constraints by about 33% over the power spectrum alone, with roughly two-thirds of that gain coming from the one-loop rather than tree-level bispectrum.
  • Marginalizing over new physics parameters (Neff, self-interacting neutrinos, curvature, varying electron mass) degrades the S4+MegaMapper neutrino constraint by less than about 15%, so the projected sensitivity is nearly model-independent.
  • The forecast shifts of Σmν from a 1σ shift in new physics parameters stay at about 1–4 meV for S4+MegaMapper, meaning a future measured value would not be significantly biased by these extensions.

Reading between the lines

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

  • The assumed roughly 50% systematic from Gaussian covariance and neglected Alcock-Paczynski and window effects suggests real analyses may yield weaker constraints; testing the pipeline on BOSS-like mocks would quantify this.
  • The redshift-scaling of EFT parameters from BOSS is an untested extrapolation at z≈2–5; calibrating the one-loop model against N-body simulations with massive neutrinos at those redshifts would directly test the kmax reach behind the 7 meV projection.
  • The lognormal Fisher treatment of Σmν and the correlation-based shift estimates could be verified by full MCMC runs with shifted fiducial values, which would also probe non-Gaussian posteriors.
  • The projected gain from the one-loop bispectrum hints that higher-order statistics (two-loop power spectrum, higher-N point functions) could push sensitivities further, though with more nuisance parameters to marginalize.
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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. This paper presents Fisher forecasts for the sum of neutrino masses using one-loop EFTofLSS predictions for the galaxy power spectrum and bispectrum, combined with CMB forecasts from Planck and Stage-4 experiments and LSS forecasts for DESI and MegaMapper. The headline results are a projected 1-sigma sensitivity of 15 meV for Planck+DESI and 7 meV for S4+MegaMapper, with the one-loop bispectrum contributing about 10% and 30% of the constraining power, respectively. The paper also considers four theory extensions (extra relativistic species, neutrino self-interactions, curvature, and a time-varying electron mass) and quantifies the shift in the inferred neutrino mass induced by a 1-sigma shift in each new-physics parameter. The analysis pipeline follows Ref. [146], uses public Boltzmann and sampling codes, and includes an analytic Fisher cross-check in Appendix A.

Significance. If taken at face value, the forecasts are timely and useful: they extend earlier power-spectrum-only forecasts by including the one-loop bispectrum, and they provide a quantitative, if approximate, assessment of the robustness of neutrino-mass sensitivities to several motivated new-physics directions. The manuscript is transparent about its main limitations: Section 4.1 states that the Gaussian covariance and neglected Alcock-Paczynski/window effects may make the Fisher constraints about 50% tighter than a full analysis, and footnote 12 explicitly limits the shift estimates. The inclusion of an analytic Fisher estimate in Appendix A and comparisons with Refs. [32-34] help situate the results. However, because the headline 7 meV sensitivity and the 30% bispectrum gain rest on the one-loop bispectrum being reliable at z_eff=4.3 up to k_max=0.76 h/Mpc with EFT parameters extrapolated from BOSS, the central numbers should be presented with a robustness band or an explicit sensitivity test.

major comments (3)
  1. [Section 4.1 / Table I] The high-redshift MegaMapper bin (z_eff=4.3, b1=6.3, k_1L_max=0.76 h/Mpc) is the bin where the one-loop bispectrum contributes most of its forecasted gain, yet the EFT parameters are obtained by redshift-scaling the BOSS best fit via Ref. [146], and no validation of the one-loop bispectrum in this high-bias, high-redshift regime is presented or cited. Since the Fisher derivatives in Eq. (10) and the Gaussian covariance are evaluated at these extrapolated values, the 30% bispectrum contribution and the 7 meV sensitivity are load-bearing on this assumption. I ask for a robustness test that degrades k_max for this bin (for example to the tree-level reach of 0.28 h/Mpc or to an intermediate 0.5 h/Mpc) and/or widens the EFT priors specifically for this bin, reporting the resulting sigma_Sigma_mnu. The prior-widening check in Appendix B covers only the Planck+DESI power-spectrum case and does not address this concern.
  2. [Section 4.1 / Eqs. (9)-(10)] The covariance is a Gaussian, diagonal approximation with no power-spectrum-bispectrum cross-covariance, and Alcock-Paczynski and window-function effects are neglected; the text estimates that these approximations make the Fisher constraints about 50% tighter than a full analysis. This systematic uncertainty is comparable to the 30% bispectrum gain quoted in the abstract and to the difference between 7 and 10 meV. I recommend that the abstract and Section 5 quote the central forecasts with this systematic explicitly attached, for example as a 50% pipeline uncertainty on the Fisher numbers, or that a shortened-k_max analysis be presented as a more conservative headline.
  3. [Section 4.4d / Table V / footnote 12] The claimed O(1) meV suppression of new-physics shifts for S4+MegaMapper is obtained from the linear-response formula Delta_Sigma = corr * sigma evaluated at the fiducial zero-new-physics point, and footnote 12 states that this is only an estimate requiring a full MCMC with a shifted fiducial for a comprehensive study. The non-Gaussian behavior visible in the Planck+DESI delta_m_e case, where the correlation changes sign between the CMB-only and combined analyses, shows that the linear correlation estimate can be fragile. Because this shift estimate is one of the two central claims in the abstract, I recommend either computing the Fisher matrix at a representative 1-sigma-shifted fiducial for the new-physics parameters or explicitly downgrading the claim to an approximate linear-response estimate.
minor comments (5)
  1. [Section 2b] The sentence starting 'the best fits of Planck and BOSS analyses are not compatible' contains a broken reference placeholder '[ ? ]' and needs a proper citation.
  2. [Section 4.2] In the MegaMapper bullet, the text says 'We use the same redshift binning, kmax, linear bias, and shotnoise specifications for DESI as outlined in Table 3 of [146]'; this should refer to MegaMapper, not DESI.
  3. [Abstract / Section 4.4b / Section 5a] The bispectrum gain is reported as 'about 10% and 30%' in the abstract, '15% and 25%' in Section 4.4b, and '33%' in Section 5a; please define the baseline for each percentage (power-spectrum-only, tree-level bispectrum, or Fisher-information fraction) so the numbers can be compared consistently.
  4. [Table VI] The row for 'this work' lists 17 meV for Planck+DESI with P_1-loop, while Table II gives 15 meV for the P+B analysis; this is not contradictory if Table VI is power-spectrum-only, but the table entry should state this explicitly.
  5. [Eq. (11)] The symbol sigma is used both for the log-space standard deviation of the lognormal distribution and for the final 1-sigma bound; please distinguish these two quantities notationally.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the forecast is computed from a fixed fiducial model and external EFT inputs; the self-citation cluster is methodological, not load-bearing.

full rationale

The paper's derivation chain is a Fisher forecast: Eq. (8) defines the Fisher matrix from theory derivatives and covariance, and Eqs. (9)-(10) evaluate it at a fixed fiducial cosmology and a fixed set of EFT parameters. The sensitivity sigma_Sigma_mnu is the inverse Fisher diagonal element, so it is computed rather than fitted: no term in the Fisher matrix is calibrated to the target sensitivity, and the Sigma_mnu response enters through the CLASS linear power spectrum and the fnu-dependent EFT kernels, not through a parameter fitted to Sigma_mnu. The main numerical dependencies on prior work are the one-loop bispectrum of Ref. [56], the loop-integral code of Ref. [143], the BOSS-calibrated EFT priors of Ref. [144], and the survey specifications, kmax reach, and redshift-scaling prescription of Ref. [146]. Several of these references share authors with the present paper (Refs. [56], [143], [144], and [146] include P. Zhang or H. Zheng), so there is a self-citation cluster. However, those cited results are prior public analyses, with the BOSS fits of Ref. [144] being externally falsifiable against survey data, and the present forecasts use them as inputs rather than as a way of re-deriving the neutrino-mass sensitivity. The shift Delta_Sigma_mnu = rho(X, Sigma_mnu) sigma_Sigma_mnu is explicitly presented as an estimate from the 2D posterior correlation, not as a fitted prediction. The dominant caveats, namely the unvalidated one-loop bispectrum at kmax = 0.76 h/Mpc at z = 4.3, the Gaussian covariance approximation, and the neglected AP and window effects, are accuracy and robustness concerns rather than circularity. No step was found in which a prediction reduces by construction to its own inputs or to a fitted parameter, so the score is set to 2 only to acknowledge the presence of a self-citation cluster that is not load-bearing in a circular sense.

Assumptions & free parameters 4 free parameters · 8 assumptions · 0 invented entities

The forecast rests on the EFTofLSS framework, Fisher approximations, and extrapolation of EFT parameters from BOSS to higher redshifts. The quoted sensitivities therefore inherit the systematic uncertainties of these modeling choices, which the authors estimate at the ~50% level. No new particles or forces are introduced; the new physics models are existing extensions of the standard model.

free parameters (4)
  • Fiducial Σmν = 0.06 eV (normal ordering minimal mass) = 0.06 eV
    The Fisher matrix is evaluated at this fiducial; the log-normal conversion from σ(log Σmν) to linear space depends on it. Chosen by hand, not fitted.
  • Perturbativity prior cap on one-loop contributions = Set by two-loop estimate relative to data error
    Section 4.1 and Appendix B: this prior restricts EFT predictions to the physically allowed region and affects the Fisher matrix, especially at low k. Its definition involves a chosen threshold.
  • EFT parameter priors widths = Width 2 (or 4 for specific parameters) on prior
    Appendix B: Gaussian priors assigned to EFT parameters; doubling the widths changes neutrino bounds by up to 8%, so the results are sensitive to this choice.
  • kmax for each redshift bin = DESI: 0.18/0.23 h/Mpc; MegaMapper: 0.36/0.76 h/Mpc (Table I)
    The theory reach kmax is estimated by matching the integrated theory noise to data noise as in Ref. [146, Eq. (2.26)]. This determines how many modes are included and is a key factor in the projected sensitivity.
assumptions (8)
  • standard math Fisher information matrix approximates the parameter covariance under Gaussian likelihoods.
    Used throughout Section 4.1 to derive constraints from Eq. (8) and the covariance matrices.
  • domain assumption EFTofLSS at one loop provides accurate predictions for galaxy power spectrum and bispectrum on the analyzed scales.
    This is the foundation of the forecast; introduced in Section 3 and used in all Fisher matrices. The validity is assumed and only tested through the perturbativity prior.
  • domain assumption Massive neutrino effects are captured by replacing the linear matter power spectrum with (1-f_nu)^2 P_cb.
    Section 3g states this is a good approximation at fraction of f_nu, but it neglects scale-dependent bias corrections of order 0.2-0.5 f_nu.
  • domain assumption The power spectrum and bispectrum covariances are Gaussian and their cross-covariance is negligible.
    Section 4.1: 'we use the Gaussian approximation... together with the cross-covariance... As such, we simply add their Fisher matrices.'
  • domain assumption The Alcock-Paczynski effect and survey window function can be neglected in the forecast.
    Section 4.1: 'our Fisher study does not account for the modeling of the Alcock-Paczynski (AP) effect and the window function... constraints are further estimated to be tightened by an additional 15% to 30%.'
  • domain assumption A 1-sigma shift in a new physics parameter X induces a shift in the inferred neutrino mass equal to corr(X, Σmν) σΣmν.
    Section 4.4d defines ΔΣmν = ρ(X,Σmν)σΣmν, and footnote 12 notes this is only an estimate requiring full MCMC for validation.
  • domain assumption The EFT parameters at the redshift of DESI and MegaMapper are obtained by scaling the BOSS best-fit values following the prescription of Ref. [146].
    Section 4.1: 'The choice of scaling we apply to the EFT parameters is the same scaling... as in [146], which extrapolates the fiducial values of these parameters from the BOSS best fit to the redshift bins.'
  • domain assumption Survey specifications for DESI and MegaMapper from Refs. [146] and [48] are representative of the actual experiments.
    Section 4.2 uses the redshift binning, kmax, bias, and shot noise from these references.

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Cite this review

Pith. "Pith review of Neutrino masses from large-scale structures: future sensitivity and theory dependence." pith.science (2026). https://pith.science/paper/IOUPZS3B

@misc{pith2026241204959,
  author       = {Pith},
  title        = {Pith review of: Neutrino masses from large-scale structures: future sensitivity and theory dependence},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IOUPZS3B}},
  note         = {Machine review of arXiv:2412.04959}
}
abstract

In the incoming years, cosmological surveys aim at measuring the sum of neutrino masses $\Sigma m_\nu$, complementing the determination of their mass ordering from laboratory experiments. In order to assess the full potential of large-scale structures (LSS), we employ state-of-the-art predictions from the effective field theory of LSS (EFTofLSS) at one loop to perform Fisher forecasts on the sensitivity (combining power spectrum and bispectrum) of ongoing and future surveys (DESI, MegaMapper) in combination with CMB measurements (Planck, Litebird and Stage-4). We find that the 1$\sigma$ sensitivity on $\Sigma m_\nu$ is expected to be 15 meV with Planck+DESI, and 7 meV with S4+MegaMapper, where $\sim 10\%$ and $30\%$ of the constraints are brought by the one-loop bispectrum respectively. To understand how robust are these bounds, we explore how they are relaxed when considering extensions to the standard model, dubbed `new physics'. We find that the shift induced on $\Sigma m_\nu$ by a $1\sigma$ shift on new physics parameters (we consider extra relativistic species, neutrino self-interactions, curvature or a time-evolving electron mass) could be $\mathcal O(10)$ meV for Planck+DESI, but it will be suppressed down to $\mathcal O(1)$ meV in S4+MegaMapper. Our study highlights the quantitative impact of including the bispectrum at one loop in the EFTofLSS, and the robustness of the sensitivity to $\Sigma m_\nu$ against potential new physics thanks to the synergy of cosmological probes.

Figures

Figures reproduced from arXiv: 2412.04959 by the authors.

Figure 1
Figure 1. FIG. 1: Forecast of uncertainty on Σ [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Constraints on cosmological parameters for S4 [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Summary of 68% (thick blue) and 95% (thin [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Constraints on cosmological parameters for S4 + [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 6
Figure 6. Figure 6: FIG. 6: Summary of Σ [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: Posteriors for Ω [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8: Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]
Figure 11
Figure 11. Figure 11: FIG. 11: Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p013_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12: Relative differences in the galaxy power [PITH_FULL_IMAGE:figures/full_fig_p017_12.png]
Figure 13
Figure 13. Figure 13: FIG. 13: Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p018_13.png]

Discussion (0). Continue with ORCID to comment.

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