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Dark Neutrino interactions phase out the Hubble tension

T0 review · 3 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Dark neutrino scattering cancels the neutrino-induced phase shift and reduces the Hubble tension to 2.1σ.

desk verdict The phase-shift mechanism is real, but the 2.1σ headline relies on the least aggressive data cut and a non-Gaussian posterior; the robust improvement is closer to 2.9σ. read the letter →

arxiv 1908.09843 v2 pith:OREPC4UN submitted 2019-08-26 hep-ph astro-ph.CO

Subhajit Ghosh , Rishi Khatri , Tuhin S. Roy This is my paper · ORCID
classification hep-phastro-ph.CO
keywords darkneutrinointeractionsHubbletensionCMBacousticphaseshiftfree-streamingmatter-neutrinoscatteringmatterpowerspectrumtwo-componentcosmologicalparameterestimation
topics Dark MatterThe Hubble Tension
open problems Dark MatterThe Hubble Tension
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

The paper proposes a new way to relieve the Hubble tension: rather than changing the expansion history or the sound horizon, it shifts the phase of the acoustic oscillations in the cosmic microwave background. The authors build a minimal model, Dark Neutrino Interactions (DNI), in which a small fraction of dark matter scatters standard left-handed neutrinos with a temperature-independent cross-section, stopping them from free streaming while keeping the effective number of relativistic species at its standard value. Fitting this cosmology to CMB and galaxy-survey data, they find the tension between the inferred $H_0$ and the local distance-ladder measurement drops from about $3.8\sigma$ in $\Lambda$CDM to roughly $2.1\sigma$, and that zero interaction strength is disfavoured at more than $3\sigma$ once the local measurement is included. If the model is right, the Hubble tension is not a crisis of the cosmological model but a direct signal of new neutrino interactions.

What carries the argument

The load-bearing mechanism is the scale-dependent acoustic phase shift $\varphi$. In $\Lambda$CDM, free-streaming neutrinos add a positive phase to the photon transfer function $\cos(kr_*+\varphi)$; DNI removes most of that phase by keeping neutrinos coupled to a subdominant dark-matter component $\chi$ through elastic scattering up to recombination. The interaction is written as an electroweak-invariant effective operator involving the Higgs and lepton doublets with a messenger $\psi$, and the controlling parameter is $fu$, the product of the interacting-dark-matter fraction and a Thomson-normalized cross-section per unit mass. Near-degeneracy of the messenger and $\chi$ masses makes the cross-section independent of neutrino temperature, which is what lets even a modest coupling postpone decoupling to late times; at $fu\sim 0.02$ the negative phase shift grows with multipole almost exactly as required to offset a larger $H_0$.

What would settle it

Measure the neutrino--dark-matter scattering cross-section as a function of neutrino temperature over the MeV-to-eV range: if it falls with temperature rather than staying constant, the DNI phase shift is erased before recombination. On the observational side, a galaxy survey reaching roughly one-percent precision in the matter power spectrum should detect the predicted few-percent enhancement and BAO phase shift at $k \simeq 0.1\,h\,\mathrm{Mpc}^{-1}$; the absence of that signal at that precision would rule out $fu\gtrsim 0.01$.

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Extended reading notes

Core claim

The central claim is that the Hubble tension can be solved by undoing the phase shift that free-streaming neutrinos imprint on the CMB acoustic peaks. In $\Lambda$CDM the photon transfer function is approximately $\cos(kr_*+\varphi)$ with $\varphi>0$ from neutrinos, and raising $H_0$ while holding physical densities fixed reduces the angular diameter distance; DNI supplies a scale-dependent negative phase shift, larger at higher multipoles, that almost exactly compensates. The model uses two-component dark matter so that only a small fraction $f$ interacts with neutrinos, leaving the dark-matter power spectrum nearly unchanged, and its only cosmological effect is the removal of neutrino free-streaming. Fitting the model to CMB data plus the full-shape galaxy power spectrum up to $k=0.12\,h\,\mathrm{Mpc}^{-1}$ reduces the tension to $2.1\sigma$ with a non-Gaussian measure, with best-fit $H_0\approx 70$ km s$^{-1}$ Mpc$^{-1}$ and an acoustic scale $\theta_*$ about $15\sigma$ away from its $\Lambda$CDM value. The paper therefore concludes that nonzero neutrino--dark-matter interactions are already preferred by the data.

Load-bearing premise

The whole mechanism rests on the neutrino--dark-matter scattering cross-section being independent of neutrino temperature all the way down to recombination, which the model obtains only by assuming the messenger and the interacting dark-matter component are nearly degenerate in mass; if a complete ultraviolet realization does not enforce that degeneracy, the late-time coupling disappears and the compensating phase shift does not happen.

Editorial extensions

If this is right

  • With the CMB and galaxy data restricted to $k\le 0.12\,h\,\mathrm{Mpc}^{-1}$, the tension falls from about $3.8\sigma$ in $\Lambda$CDM to $2.1\sigma$; cutting the galaxy data at larger $k$ still keeps it below $3\sigma$.
  • A larger $H_0$ is achieved without changing the number of relativistic species, so the model does not rely on extra radiation or modified early-time expansion.
  • Once the local distance-ladder value is included, zero neutrino interaction ($fu=0$) is excluded at more than $3\sigma$, making the Hubble tension evidence for new neutrino interactions.
  • The model predicts a modified CMB B-mode spectrum that future polarization experiments could detect if the tensor-to-scalar ratio is near current limits.
  • The matter power spectrum receives a few-percent scale-dependent enhancement plus a BAO phase shift, which future surveys at roughly one-percent precision could observe.

Reading between the lines

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

  • The phase-shift mechanism is more general than the specific operator: any subdominant dark-matter component with temperature-independent elastic scattering off neutrinos should produce a similar scale-dependent peak shift, making DNI a template for a broader model class.
  • Because standard BAO likelihoods assume the $\Lambda$CDM phase shift, they cannot be applied to this class of models; re-analyzing existing BAO data with the phase shift left free could strengthen or weaken the preference for $fu>0$.
  • The reported $2.1\sigma$ uses a non-Gaussian tension measure, so direct comparisons with Gaussian $|H_0^{\rm CMB}-H_0^{\rm local}|/\sigma$ numbers require converting between conventions.
  • The near-degenerate mass condition ties the cosmology to a narrow parameter region that laboratory searches for sub-MeV dark matter or low-energy neutrino scattering could in principle probe.
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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 / 6 minor

Summary. The paper proposes a new mechanism, Dark Neutrino Interactions (DNI), to alleviate the Hubble tension. A small fraction of dark matter interacts with standard left-handed neutrinos through a nearly degenerate mediator, making the scattering cross-section temperature-independent so that neutrinos remain coupled until recombination. This suppresses the standard free-streaming phase shift in the CMB acoustic peaks, and the authors show that this phase shift has the scale dependence needed to compensate for a larger H0. They implement the model in CLASS, run MCMC analyses with Planck 2015 and WiggleZ power-spectrum data (using three k-cuts W1, W2, W3), and report that the Hubble tension is reduced to about 2.1σ for the W1 cut, with no-interaction (fu=0) disfavoured at more than 3σ when SH0ES data are included. They also predict modifications to CMB B-modes and the matter power spectrum observable by future experiments.

Significance. If the headline result were robust, this would be a valuable contribution: it introduces a qualitatively new way to address the Hubble tension by altering the acoustic phase shift rather than only the sound horizon or late-time expansion, and it makes concrete, testable predictions for B-modes and large-scale structure. The analysis is competently performed with public codes (CLASS, Monte Python), the modified CLASS code is made publicly available, and the physical mechanism is clearly explained and internally consistent. The main weakness is statistical: the central quantitative claim of a ~2.1σ tension reduction is not robust to the choice of WiggleZ k-cut and depends on a non-Gaussian secondary peak in the H0 posterior, as the authors themselves state. The paper needs to present a more conservative and dataset-robust measure of the tension reduction.

major comments (3)
  1. [Section IV, Fig. 4 (right) and text after the definition of d] The central claim that the Hubble tension reduces to approximately 2.1σ is not robust. The text states that the small secondary peak in the P15+W1 posterior causes a jump in d, reducing the tension to 2.1σ, while the same chains with W2 and W3 give 2.93σ and 2.75σ, respectively. A simple Gaussian estimate from Table I (H0 = 69.39 ± 0.68 for P15+W1 versus SH0ES = 74.03 ± 1.42) gives about 2.9σ, consistent with the W2/W3 values. Since the abstract and conclusions highlight the 2.1σ number as the main result, the paper overstates the model's performance. The authors should either report the more conservative ~2.9σ value as the headline tension reduction, use a properly Gaussianized or likelihood-based tension statistic, or explicitly and prominently qualify that 2.1σ is an artifact of the W1 k-cut and a non-Gaussian secondary peak.
  2. [Section V, Conclusions and Fig. 5] The claim that fu=0 is disfavoured at more than 3σ is based solely on the P15+W1+SH0ES posterior for fu. The paper does not show whether this exclusion persists for the W2 and W3 k-cuts, which are the same cuts that give the more stable 2.9σ tension values. Given that the fu posterior is highly non-Gaussian and that the W1 cut is the one producing the anomalous secondary peak, the >3σ exclusion for no-interaction should be checked against the other data cuts and ideally with a profile-likelihood or Bayesian evidence calculation. Without this, the conclusion that 'we might have found evidence of new interactions of neutrinos' is not supported by a robust statistical analysis.
  3. [Section III, Eq. (6) and text following] The entire mechanism relies on the temperature independence of the neutrino–dark matter cross-section, which is achieved by assuming the messenger ψ and dark matter χ are nearly degenerate in mass. If this degeneracy is not realized in a UV completion, the cross-section will inherit a temperature dependence, the late-time coupling will disappear, and the scale-dependent phase shift that compensates the Hubble tension will not occur. The paper cites Ref. [80] for a possible UV completion, but the present manuscript presents this as a proof-of-principle. This is a model-building caveat rather than an internal inconsistency, but it should be stated more prominently as a key assumption that must be satisfied for the proposed solution to work.
minor comments (6)
  1. [Author line] The author line contains a duplicated word: 'Rishi Khatri, 1,† and and Tuhin S. Roy' should read '... and Tuhin S. Roy'.
  2. [Section IV, definition of tension statistic] The definition of d using t-dependent credible-interval widths is nonstandard and the paper should clarify that a Gaussianized comparison from the same chains gives a different answer; the text should note this explicitly when the 2.1σ value is discussed.
  3. [Section V, Conclusions] The phrase 'We therefore might have found evidence of new interactions of neutrinos in the Hubble tension' is stronger than the statistical analysis supports; it should be qualified in light of the W2/W3 and Gaussianized results.
  4. [Figure 4, left panel] The left panel appears to lack axis labels in the description; it would be clearer to label the horizontal axis as fu and the vertical axis as H0 (km/s/Mpc).
  5. [Appendix A, Fig. 7] The axis label '100thetas' should be formatted as '100θ∗' for consistency with the table.
  6. [References] The paper uses Planck 2015 data; given that Planck 2018 results are cited in Ref. [2], the analysis should either be updated to Planck 2018 or the choice of Planck 2015 should be justified.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the DNI phase-shift mechanism is derived from standard acoustic physics and tested against external data; the main caveats are model assumptions and a fragile tension statistic, not circular reasoning.

full rationale

The paper's central derivation is not circular. The phase-shift relation in Eq. (1) and the required shift in Eq. (2) follow from standard acoustic oscillation theory, and the DNI effect on CMB peak positions is computed with a modified CLASS code rather than imposed to match the data. The parameters f and u are fitted with flat priors and then used to infer H0, which is standard parameter inference rather than a 'prediction' that reduces to its inputs. The 2.1σ tension reduction is obtained from a non-Gaussian posterior and an explicitly defined t-dependent statistic, and the paper transparently reports that W2 and W3 cuts give 2.93σ and 2.75σ and that a secondary peak causes the jump in d; this is a statistical robustness concern, not circularity. The only notable self-citation is Ref. [80], used to justify the temperature-independent neutrino-DM cross-section that requires nearly degenerate mediator and DM masses. This is a model-building assumption supported by a prior calculation by the same authors, and it does not simply restate the Hubble-tension result; it is a microphysical input with stated assumptions. Under the stated rules, this is independent support rather than load-bearing circularity, so the score is low despite the model-dependence of the headline significance claim.

Assumptions & free parameters 1 free parameters · 6 assumptions · 2 invented entities

The central claim depends on two new particles (χ and ψ) and an effective operator, plus the assumptions of temperature-independent scattering, small f, and the validity of Halofit. The only genuinely fitted new physics parameter is the combination fu; the other quantities are model inputs or prior assumptions.

free parameters (1)
  • fu (effective interaction strength) = best-fit 0.0187 (P15+W1) and 0.0232 (P15+W1+SH0ES) for fixed f = 10^-3; varied freely in other runs
    This product controls the neutrino scattering rate and is the key new physics parameter varied in the MCMC. It determines the phase shift and hence the shift in H0.
assumptions (6)
  • domain assumption Flat ΛCDM background with physical densities fixed when varying H0
    Used in Section II to derive Eq. 2; the authors note a curvature term would not allow the constant shift compensation.
  • domain assumption Neutrinos are massless and all three flavors interact with equal strength
    Section III; a consequence of the chosen effective operator, not an empirical fact.
  • ad hoc to paper Mediator ψ and dark matter χ are nearly degenerate in mass, making the cross-section temperature-independent
    Section III; required for the scale-dependent phase shift. No UV completion is given; only a citation to the authors' prior work [80].
  • domain assumption Small f approximation: modifications to total DM transfer functions are O(f^2) and negligible
    Section III; this isolates the effect to neutrino free streaming, but is only valid for f << 1.
  • domain assumption Halofit nonlinear correction is valid for DNI cosmology
    Section IV; justified only by the smallness of the modifications, not by tests.
  • standard math CMB peak positions follow cos(kr* + φ) with a neutrino-induced phase shift φ
    Section I, Eq. 1; standard acoustic oscillation theory from Sunyaev-Zeldovich and Peebles-Yu.
invented entities (2)
  • χ, interacting dark matter component independent evidence
    purpose: Scatters with neutrinos via the effective operator to stop free streaming
    The model predicts B-mode modifications and matter power spectrum enhancements that future observations can test, though no direct detection is provided.
  • ψ, messenger (flavor triplet) independent evidence
    purpose: Mediates the neutrino-dark matter interaction
    Same observational handles as χ; collider constraints are weak for Λ around 2.5 TeV.

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Cite this review

Pith. "Pith review of Dark Neutrino interactions phase out the Hubble tension." pith.science (2026). https://pith.science/paper/OREPC4UN

@misc{pith2026190809843,
  author       = {Pith},
  title        = {Pith review of: Dark Neutrino interactions phase out the Hubble tension},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OREPC4UN}},
  note         = {Machine review of arXiv:1908.09843}
}
abstract

New interactions of neutrinos can stop them from free streaming even after the weak interaction freeze-out. This results in a phase shift in the cosmic microwave background (CMB) acoustic peaks which can alleviate the Hubble tension. In addition, the perturbations in neutrinos do not decay away on horizon entry and contribute to metric perturbation enhancing the matter power spectrum. We demonstrate that this acoustic phase shift can be achieved using new interactions of standard left-handed neutrinos with dark matter without changing the number of effective relativistic degrees of freedom. Using Planck CMB and the WiggleZ galaxy survey $ (k\le 0.12 h \ {\rm Mpc}^{-1} ) $ data, we demonstrate that in this model the Hubble tension reduces to approximately $ 2.1 \sigma$. Our model predicts potentially observable modifications of the CMB B-modes and the matter power spectrum that can be observed in future data sets.

Figures

Figures reproduced from arXiv: 1908.09843 by the authors.

Figure 1
Figure 1. FIG. 1: CMB temperature (TT) power spectrum around first six acoustic peaks. The leftmost solid red line is the [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Comparison of [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Shift of the position of peaks of CMB TT [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: (centre) that stronger neutrino interaction favours higher H0. The 2D contours clearly indicates that data prefer small f (. 10−2 ) and, as discussed above, for small f the results (limits) become independent of the value of f (Eq. 7). These are general features of DNI…
Figure 5
Figure 5. Figure 5: FIG. 5: Left: 1-D posterior for [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: Absolute change in CMB B-modes [primordial [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: Triangular plot for ΛCDM and DNI cosmologies (with [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]

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