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Joint 21-cm and CMB Forecasts for Constraining Self-Interacting Massive Neutrinos

T0 review · 3 major / 4 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read The 21-cm power spectrum can probe neutrino self-interactions beyond the reach of CMB experiments, and combining 21-cm with CMB-S4 breaks the neutrino-mass versus self-coupling degeneracy.

desk verdict First 21-cm power-spectrum forecast for neutrino self-interactions; the joint HERA+CMB-S4 numbers are solid, but the HERA-only headline case depends on a popII-only source model that the paper itself shows is fragile. read the letter →

arxiv 2504.15348 v2 pith:QGEDCIJG submitted 2025-04-21 astro-ph.CO

Sarah Libanore , Subhajit Ghosh , Ely D. Kovetz , Kimberly K. Boddy , Alvise Raccanelli This is my paper · ORCID
classification astro-ph.CO
keywords 21-cmcosmologyneutrinoself-interactionsmassiveneutrinoscosmicdawndarkagesFisherforecasthalomassfunctionCMB-S4
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 whether the 21-cm power spectrum—the radio signal from neutral hydrogen during cosmic dawn and the dark ages—can measure the self-interaction strength of massive neutrinos, a parameter that current and planned CMB observations constrain only weakly. The argument is that self-interacting neutrinos imprint scale-dependent bumps and suppressions on the matter power spectrum at $k > 0.1\,{\rm Mpc}^{-1}$, which change the abundance of the small and intermediate halos that host the first galaxies, and those changes propagate into the 21-cm signal. Using Fisher forecasts built from a Boltzmann solver that includes neutrino self-interactions and a semi-analytic 21-cm simulation, the paper finds that the HERA array at design sensitivity can improve on existing constraints on the coupling $G_{\rm eff}$ and reach values of the coupling beyond CMB experiments. The central quantitative result is that a joint HERA+CMB-S4 analysis yields 2-$\sigma$ uncertainties of roughly 8%–14% on $\log_{10} G_{\rm eff}$ for strong, moderate, and mild self-interaction models, while a futuristic lunar array could reach 1%–5%. This matters because recent cosmology hints at a bimodal posterior for $G_{\rm eff}$, and the neutrino mass–coupling degeneracy is precisely the kind of correlation that joint 21-cm and CMB data can break.

What carries the argument

The load-bearing chain runs from a four-Fermi effective operator $\mathcal{L} \supset \frac{1}{2}G_{\rm eff}(\bar\nu\nu)(\bar\nu\nu)$, whose coupling $G_{\rm eff}$ controls how long neutrinos behave as a fluid instead of free streaming. A modified Boltzmann solver computes the resulting scale-dependent matter power spectrum $P_m(k,z)$; that spectrum enters the Sheth–Tormen halo mass function through the variance $\sigma^2(M_h,z) = \int_0^\infty (dk/k) P_m(k,z) W_R^2(k)$, and the halo abundance determines the star formation rate density that drives the 21-cm signal in a semi-analytic simulation. The Fisher matrix then converts simulated sensitivities into forecast uncertainties. The mechanism that carries the argument is this mapping from small-scale power features to halo-abundance features to 21-cm brightness fluctuations, rather than any single direct observable.

What would settle it

Measure the 21-cm power spectrum at $z\simeq 13$ with HERA at design sensitivity: if the data match $\Lambda$CDM while the mild-coupling model predicts a visible boost in the abundance of $10^8$–$10^{10}\,M_\odot$ halos that shifts the signal, the forecast's central claim is falsified. A weaker but still decisive test is the CMB-S4 bound on $\log_{10} G_{\rm eff}$ for the mild model, which the paper forecasts at 534% uncertainty; a much tighter bound would indicate the 21-cm complementarity is not needed.

Watch

Extended reading notes

Core claim

Self-interacting neutrinos delay the onset of free streaming. Modes that enter the horizon before self-decoupling experience suppressed growth, while modes entering near self-decoupling are boosted, producing a scale-dependent feature in the linear matter power spectrum. The paper shows that this feature propagates through the halo mass function to the star formation rate density and hence to the 21-cm power spectrum, making cosmic dawn an indirect probe of scales $k \sim 1$–$100\,{\rm Mpc}^{-1}$ that CMB observations cannot reach directly. The paper's central claim is that HERA alone outperforms CMB-S4 for moderate and mild self-interactions, CMB-S4 alone is better for the strong case, and adding HERA to CMB-S4 improves the constraint on $\log_{10} G_{\rm eff}$ in all three benchmark models, with the joint analysis reaching $\sim 10\%$ 2-$\sigma$ uncertainties. During the dark ages, where astrophysics is absent, the paper forecasts that a large lunar interferometer can reach percent-level constraints on $\log_{10} G_{\rm eff}$.

Load-bearing premise

The forecast collapses if the semi-analytic astrophysical model that turns the matter power spectrum into the 21-cm signal—the halo mass function, star formation efficiencies, and reionization history—does not accurately predict how the abundance of small and intermediate halos changes when the power spectrum is modified.

Editorial extensions

If this is right

  • HERA at design sensitivity should improve current constraints on the neutrino self-coupling and probe couplings below the reach of current and future CMB experiments.
  • For the moderate- and mild-coupling models, HERA alone is forecast to beat CMB-S4; for the strong-coupling model, CMB-S4 is more sensitive, but the pair together is best in all cases.
  • The joint HERA+CMB-S4 analysis breaks the degeneracy between the sum of neutrino masses and $\log_{10} G_{\rm eff}$, yielding 2-sigma uncertainties of 8%, 11%, and 14% for the strong, moderate, and mild models in the baseline astrophysical scenario.
  • A large lunar radio array probing the dark ages could reach 2-sigma uncertainties of 1%–5% on $\log_{10} G_{\rm eff}$, without astrophysical contamination.
  • Including population III stars in the astrophysical model generally weakens the cosmic-dawn constraints because of additional free parameters, but it improves the mild-coupling case by helping to break the mass–coupling degeneracy.

Reading between the lines

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

  • If the forecast chain is right, the same halo-abundance route should make cosmic-dawn 21-cm observations sensitive to other models that alter small-scale power, such as warm dark matter or dark matter–baryon interactions; the Fisher setup here is a template for those searches.
  • A direct test of the mechanism would be to compare the scale-dependent shape of the 21-cm power spectrum at $z\sim 13$: the moderate- and mild-coupling models predict a boost in halo abundance in the $10^8$–$10^{10}\,M_\odot$ range, so the signal should rise faster than in $\Lambda$CDM even if the overall amplitude is degenerate with astrophysics.
  • The dark-ages forecast assumes linear evolution of the density field above $z>35$; including the baryon–dark-matter relative-velocity mode coupling, which the paper notes is neglected, could slightly boost the large-scale signal for the mild-coupling model and improve the lunar-array constraints rather than degrade them.
  • The paper's claim that CMB-S4 breaks the $M_\nu$–$G_{\rm eff}$ degeneracy for the mild model implies that any future small-scale probe with different redshift coverage, for example a galaxy survey at moderate redshift, should show a similar complementarity with 21-cm data.
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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 / 4 minor

Summary. The paper presents Fisher-matrix forecasts for constraints on the neutrino self-coupling strength G_eff from 21-cm power-spectrum measurements, alone and in combination with CMB-S4. The 21-cm signal is modeled with 21cmFirstCLASS, initialized with transfer functions from the modified Boltzmann code nuCLASS, for three fiducial models: strong (SIν), moderate (MIν), and mild (mIν) self-interactions. For cosmic dawn, the forecast uses HERA design sensitivity and two astrophysical scenarios (popII-only and popII+popIII); for the dark ages, it uses two lunar interferometer configurations (Lunar D and LRA1). The main quantitative claims are that HERA at design sensitivity can improve on CMB-only constraints for moderate couplings, that HERA+CMB-S4 breaks the M_ν–G_eff degeneracy and reaches ~8–14% (2σ) on log10(G_eff/MeV^-2), and that LRA1+CMB-S4 reaches ~1–4%.

Significance. If the forecasts hold, the paper would be the first systematic demonstration that 21-cm observations can probe neutrino self-interactions, complementing CMB and LSS probes and opening a new observational window on beyond-Standard-Model neutrino physics. The analysis is technically careful in several respects: the nuCLASS code is made public, the CMB part is validated against the CMB-S4 Science Book and against the earlier forecast of Ref. [32], the CMB settings are conservative (single channel, ℓ<3000), and the Fisher formalism is applied consistently. The main weakness is that the central HERA claims are conditional on an unvalidated semi-analytic astrophysical model, and the paper's own Table IV shows that the HERA-only results change by an order of magnitude when popIII stars are added. The dark-ages forecasts additionally rely on an acknowledged linear-evolution approximation at z>35; the paper argues this is subdominant, but does not provide a quantitative robustness test.

major comments (3)
  1. [§V.2, Table IV] The paper's headline claim that HERA can improve upon existing constraints on G_eff is not robust to the treatment of popIII stars. In Table IV, the HERA-only 2σ constraint on log10(G_eff/MeV^-2) for the moderate-interaction model MIν degrades from 16% (popII-only) to 176% (popII+popIII), while for SIν it degrades from 32% to 72%; for mIν it improves from 112% to 78%. Since the MIν and SIν cases are the ones that support the abstract's statement that HERA 'can improve upon existing constraints' and be sensitive 'beyond the reach of current and future CMB experiments', this statement should be qualified as conditional on the popII-only astrophysical baseline. I would ask the authors to either (a) state explicitly that the HERA-only claim applies only to the baseline scenario and is not robust when popIII sources are included, or (b) provide a physically motivated argument, backed by external data, for why the popII-only scenario is the relevant fiducial for HERA's observational window.
  2. [§III.A, Eqs. (7)–(16), (15)] The forecast chain from the linear matter power spectrum to the 21-cm signal is built on the Sheth-Tormen halo mass function (Eq. 15), the EPS-based collapse fraction (Eq. 12), and the popII/popIII star-formation prescriptions (Eqs. 7–16). This chain is applied to halos in the range M_h ~ 10^8–10^11 M_sun at z ~ 13–30, where neither the Sheth-Tormen fitting function nor the assumed mapping from halo mass to Lyα and X-ray emissivities has been validated against simulations or observations. Because the Fisher derivatives dΔ21^2/dG_eff are computed through this chain, an error in the high-redshift HMF shape or in the SFR mapping could directly bias the forecasted sensitivity, either manufacturing or erasing the scale-dependent signature. The paper itself notes (footnote 5) that stochasticity in galaxy emissivities may be non-negligible. I request a robustness test against at least one alternative HMF (e.g., a Tinker-type mass function or a simulation-calibrated fit) and an alternative SFR prescription, with the resulting shifts in the Table IV constraints reported.
  3. [§V.3, Sec. IV] The dark-ages forecasts for Lunar D and LRA1 use 21cmFirstCLASS runs in which the matter density field is evolved linearly at z>35, neglecting the mode coupling induced by the baryon–dark-matter relative velocity. The paper acknowledges this approximation and cites Ref. [127] for a ~10% effect in ΛCDM at k≲0.01 Mpc^-1, arguing that it is subdominant for the scales and redshifts considered. However, the mIν model has enhanced small-scale power (Fig. 2), which, after mode coupling, could feed power to the larger scales probed by Lunar D; the paper states this 'may slightly boost the SNR' but does not quantify it. Since the percent-level LRA1 claims are a headline result, I would like to see either a quantitative estimate of this effect for each neutrino model or a clear statement that the LRA1 constraints at k>1.5 Mpc^-1 are unaffected by the linear-evolution approximation because they use the high-resolution box.
minor comments (4)
  1. [Eq. (13)] The definition of the smoothing scale appears to have a typo: R = [3M_h/(4πρ̄_m,0)]^{-3} should presumably be R = [3M_h/(4πρ̄_m,0)]^{1/3}, the comoving radius of the top-hat window.
  2. [§V.1] The sentence comparing the forecast uncertainty to Ref. [32] says 'close to our value in Table I'; the relevant entry is in Table IV, not Table I.
  3. [§IV.A.2, Eq. (29)] In the dark-ages noise formula, the notation V_z and √(V_z k^3) is dimensionally awkward as written; please check the factors and define all symbols (Δln k, f_sky, χ(z)) at first use.
  4. [Fig. 7 caption and §IV] The right panel of Fig. 7 is said to come from 'an additional 21cmFirstCLASS simulation' without specifying the box size; Sec. IV gives L=50 Mpc and N_cell=128, but the caption should be self-contained.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the 21-cm and CMB forecasts are forward-model predictions validated against external benchmarks, not reductions to fitted inputs or self-citation chains.

full rationale

The paper's central claim is a Fisher forecast of future experimental sensitivities, not a measurement or a fit. The derivation chain is physical and non-circular: nuCLASS integrates the Boltzmann hierarchy with neutrino self-interactions (Eq. A8) to produce the matter power spectrum; 21cmFirstCLASS propagates this to the halo mass function through Eqs. (13)-(15), to the star formation rate density through Eqs. (7)-(11), and to the 21-cm power spectrum through Eqs. (4)-(6) and Appendix B. Each step is a forward model with stated inputs, and no output is used to define the quantity it is supposed to predict. The fiducial values of log10Geff are taken from independent prior analyses, not derived from the 21-cm signal. The sensitivity forecasts are computed from numerical derivatives of simulated observables (Eqs. 33 and 35), so the constraints are not fitted to the data they claim to predict. The astrophysical model is an assumption rather than a fit; the paper explicitly tests the popII versus popII+popIII scenarios and reports the resulting variation in Table IV. The CMB pipeline is validated against the CMB-S4 Science Book and against prior forecasts. Self-citations to nuCLASS, 21cmFirstCLASS, and the optical-depth treatment in Ref. [46] are citations to public code and methodology with external anchors (CLASS, 21cmFAST, and Ref. [45]); none imports a uniqueness theorem or an ansatz that by itself forces the claimed result. Model dependence of the astrophysical chain is a robustness concern, not circularity.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new particles or forces; it adopts the established self-interacting neutrino framework with a scalar mediator and the effective coupling G_eff. The main ledger items are the chosen fiducial parameters (G_eff benchmarks, SI_nu parameters from an external fit, and the astrophysical model) and the modeling chain from Boltzmann physics through the halo mass function to the 21-cm signal. The Fisher approximation and the semi-analytic 21-cm model are the most consequential assumptions for interpreting the quoted sensitivities.

free parameters (4)
  • fiducial G_eff for MI_nu = log10 G_eff = -4 (MeV^-2)
    Chosen by hand to sit near the upper bound of Ref. [48] and beyond current CMB reach; defines the forecast model in Table I.
  • fiducial G_eff for mI_nu = log10 G_eff = -5 (MeV^-2)
    Chosen by hand an order of magnitude below MI_nu to represent a beyond-reach scenario; defines the target sensitivity in Table I.
  • SI_nu cosmological parameters (n_s, N_eff, A_s, M_nu) = n_s=0.9298, N_eff=2.82, A_s=1.959e-9, M_nu=0.08 eV
    Taken from the best-fit of the Planck+BAO analysis in Ref. [48]; these parameters partially compensate the CMB effects of strong self-interactions and shape the SI_nu matter power spectrum.
  • Fiducial astrophysical model (popII-only baseline) = log10 f*,10 = -1.25, alpha*10 = 0.5, log10 fesc,10 = 1.35, log10 LX,10/SFR = 40.5
    Baseline astrophysical model for the HERA forecast, taken from Refs. [95,96]. The paper shows switching to popII+popIII changes the 2-sigma G_eff constraint for SI_nu from 32% to 72% (Table IV, Sec. V.2), so the central numbers depend on this choice.
assumptions (5)
  • domain assumption Self-interacting neutrinos are described by a 4-Fermi effective operator with coupling G_eff after integrating out an O(MeV) scalar mediator (Eqs. 1-2).
    Adopted from Refs. [24,28]; the particle physics model is not derived in this paper, and the forecast assumes this operator governs neutrino self-scattering after decoupling.
  • standard math The Boltzmann solver nuCLASS correctly implements the self-interaction collision terms following the hierarchy of Eq. (A8) with precomputed S_l kernels.
    The code is made public but no formal verification or independent reproduction is provided; the paper validates against Ref. [32] for the CMB forecast, but the 21-cm derivatives are not independently checked.
  • domain assumption The 21-cm signal is modeled by 21cmFirstCLASS using the EPS/Sheth-Tormen halo mass function (Eqs. 12-15) and the star formation rate model of Refs. [95,96] (Eq. 16), with the matter density field evolved linearly at z>35.
    Semi-numerical approximation; footnote 5 notes stochasticity in galaxy emissivities has a non-negligible effect, and Sec. V.3 acknowledges that neglect of baryon-dark-matter relative velocity mode coupling could contribute up to roughly 10% on large scales at z~30.
  • standard math The Fisher matrix formalism with Gaussian likelihood and linear derivatives is adequate for the quoted 2-sigma constraints.
    Fisher forecasts assume linear response; for the mI_nu HERA-only case the 2-sigma uncertainty on log10 G_eff is 112%, far outside the linear regime, so the Fisher result there is indicative rather than quantitative.
  • domain assumption The optical depth tau is recomputed self-consistently from the 21cmFirstCLASS ionization history using Eq. (27) and propagated via Eq. (38).
    The tau mapping from the simulation is an internal estimate; the fiducial tau values differ slightly from Ref. [48] values (Table I), and the joint CMB+21-cm constraint depends on this propagation.

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Cite this review

Pith. "Pith review of Joint 21-cm and CMB Forecasts for Constraining Self-Interacting Massive Neutrinos." pith.science (2026). https://pith.science/paper/QGEDCIJG

@misc{pith2026250415348,
  author       = {Pith},
  title        = {Pith review of: Joint 21-cm and CMB Forecasts for Constraining Self-Interacting Massive Neutrinos},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QGEDCIJG}},
  note         = {Machine review of arXiv:2504.15348}
}
abstract

Self-interacting neutrinos provide an intriguing extension to the Standard Model, motivated by both particle physics and cosmology. Recent cosmological analyses suggest a bimodal posterior for the coupling strength $G_{\rm eff}$, favoring either strong or moderate interactions. These interactions modify the scale-dependence of the growth of cosmic structures, leaving distinct imprints on the matter power spectrum at small scales, $k\,>\,0.1\,{\rm Mpc}^{-1}$. For the first time, we explore how the 21-cm power spectrum from the cosmic dawn and the dark ages can constrain the properties of self-interacting, massive neutrinos. The effects of small-scale suppression and enhancement in the matter power spectrum caused by self-interacting neutrinos propagate to the halo mass function, shaping the abundance of small- and intermediate-mass halos. It is precisely these halos that host the galaxies responsible for driving the evolution of the 21-cm signal during the cosmic dawn. We find that HERA at its design sensitivity can improve upon existing constraints on $G_{\rm eff}$ and be sensitive to small values of the coupling, beyond the reach of current and future CMB experiments. Crucially, we find that the combination of HERA and CMB-S4 can break parameter degeneracies, significantly improving the sensitivity to $G_{\rm eff}$ over either experiment alone. Finally, we investigate the prospects of probing neutrino properties with futuristic Lunar interferometers, accessing the astrophysics-free 21-cm power spectrum during the dark ages. The capability of probing small scales of these instruments will allow us to reach a percent-level constraint on the neutrino self-coupling.

Figures

Figures reproduced from arXiv: 2504.15348 by the authors.

Figure 1
Figure 1. FIG. 1. Residuals of the CMB temperature power spectrum [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Residuals of the linear matter power spectrum at [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Illustrative plot of the 21-cm global signal across cosmic history. The evolution of [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: FIG. 4. 21-cm power spectrum during cosmic dawn for fixed [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Halo mass function (top) and its residual with respect [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. 21-cm power spectrum during cosmic dawn for fixed [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. 21-cm power spectrum during the dark ages for fixed [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 8
Figure 8. Figure 8: shows the redshift-dependent cumulative signal-to-noise ratio SNR(z) = X k∈kHERA ∆2 21(k, z) σ∆2 21,CD(k, z) (28) for HERA, obtained using 21cmSense and summing over the scale range kHERA ∈ [0.05, 1.5] Mpc−1 allowed by the instrument resolution. 2. Dark ages: Lunar arr…
Figure 9
Figure 9. Figure 9: FIG. 9. Summary plot of the main results of our paper. We show forecasts for the constraining power of ∆ [PITH_FULL_IMAGE:figures/full_fig_p015_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Forecasts for the constraining power of HERA for the SI [PITH_FULL_IMAGE:figures/full_fig_p017_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11. Confidence ellipses on the neutrino parameters for Lunar D (left) and LRA1 (right) for the mI [PITH_FULL_IMAGE:figures/full_fig_p018_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12. Confidence ellipses and 2 [PITH_FULL_IMAGE:figures/full_fig_p022_12.png]
Figure 13
Figure 13. Figure 13: FIG. 13. Confidence ellipses and 2 [PITH_FULL_IMAGE:figures/full_fig_p023_13.png]

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