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Constraining the phase shift of relativistic species in DESI BAOs

T0 review · 4 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read DESI's first-year BAO data, combined with Planck, constrain the phase-shift amplitude to β_φ = 2.7^{+0.60}_{−0.67}, hinting that the phase shift may exceed the standard-model expectation.

desk verdict Solid, honest first DESI DR1 phase-shift measurement, but the 4.3σ headline is prior-driven and drops to 3.2–3.7σ under the paper's own model variations. read the letter →

arxiv 2412.05990 v2 pith:RVGNYXMG submitted 2024-12-08 astro-ph.CO

Abbé M. Whitford , Hugo Rivera-Morales , Cullan Howlett , Mariana Vargas-Magaña , Sébastien Fromenteau , Tamara M. Davis , Alejandro Pérez-Fernández , Arnaud de Mattia
show 31 more authors
Steven Ahlen Davide Bianchi David Brooks Etienne Burtin Todd Claybaugh Axel de la Macorra Peter Doel Simone Ferraro Jaime E. Forero-Romero Enrique Gaztañaga Satya Gontcho A Gontcho Gaston Gutierrez Stephanie Juneau Robert Kehoe David Kirkby Theodore Kisner Sergey Koposov Martin Landriau Laurent Le Guillou Aaron Meisner Ramon Miquel Francisco Prada Ignasi Pérez-Ràfols Graziano Rossi Eusebio Sanchez Michael Schubnell David Sprayberry Gregory Tarlé Benjamin Alan Weaver Pauline Zarrouk Hu Zou
This is my paper · ORCID
classification astro-ph.CO
keywords baryonacousticoscillationsphaseshiftfree-streamingneutrinoseffectivenumberofrelativisticspeciesDESIDR1large-scalestructurecosmologicalparameters
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 tries to measure the amplitude β_φ of the phase shift that free-streaming relativistic particles imprint on the baryon acoustic oscillation (BAO) wiggles, using DESI's first data release and an anisotropic BAO fitting pipeline. The central result is that the combined DESI BAO + Planck analysis gives β_φ = 2.$7^{{+0.60}}$_{−0.67}, suggesting β_φ > 0 at 4.3σ and larger than the standard-model value β_φ = 1 for N_eff = 3.044. If real, this would indicate a phase shift not purely sourced by standard-model neutrinos, possibly from non-standard neutrino physics or other light relics. The paper also validates the method against simulations and finds that the choice of broadband fitting method can shift β_φ by about 0.3 for power-spectrum fits, which must be controlled for future DESI data releases.

What carries the argument

The load-bearing object is the parameterization of the BAO phase shift, φ(N_eff, k) = β_φ f(k), with f(k) = φ_∞ / [1 + (k_*/k)^ξ], where φ_∞ = 0.227, k_* = 0.0324 h/Mpc, ξ = 0.872, taken from Baumann et al. (2018, 2019). The paper extends this to an anisotropic BAO fit by inserting (β_φ − 1) f(k′)/r_s into the wiggle power-spectrum template alongside the anisotropic distortion parameters α_∥ and α_⊥, and implements this in two independent codes (Barry and desilike). The combination of tracers with importance sampling, plus a Planck prior on α and α_AP, is what sharpens the constraint from β_φ = 2.7 ± 1.7 to 2.$7^{{+0.60}}$_{−0.67}.

What would settle it

Run the same DESI DR1 analysis on mocks that include a non-standard phase shift with a different scale dependence (e.g., from interacting neutrinos) and check whether the standard template recovers the input β_φ without bias. If β_φ moves toward one or the statistical significance drops under a flexible f(k), the 4.3σ result is an artifact of the assumed template rather than new physics.

Watch

Extended reading notes

Core claim

The paper's central claim is that the phase-shift amplitude β_φ can be measured with DESI DR1 BAO data using an anisotropic BAO fitting pipeline, and that the combined measurement, after adding a Planck-based prior on the BAO distortion parameters, is β_φ = 2.$7^{{+0.60}}$_{−0.67}. This is a 4.3σ preference for β_φ > 0 and about 2.6σ from the standard-model value β_φ = 1 (N_eff = 3.044). The authors interpret this as a hint of a phase shift not purely sourced by the standard-model expectation for N_eff, while noting it could be an upward statistical fluctuation and that the tension relaxes when extra model freedom (e.g., wCDM or varying A_lens) is allowed.

Load-bearing premise

The fitting assumes that the true phase shift has exactly the scale dependence given by the template f(k) in equation 17; if non-standard physics changes this shape, the fitted β_φ will absorb that difference and the quoted significance could be biased.

Editorial extensions

If this is right

  • If the 4.3σ detection is genuine, the phase shift in DESI BAOs is larger than the standard-model N_eff prediction, pointing to non-standard neutrino physics, non-adiabatic primordial fluctuations, or other free-streaming relics.
  • Allowing β_φ to vary weakens constraints on the BAO distance parameters α and α_AP because of the strong degeneracy between α and β_φ; future precise analyses may need to marginalize over β_φ to avoid biasing distance measurements.
  • The consistency between the two fitting codes and the mock validation suggest the measurement is robust at the current statistical precision, but the polynomial broadband method applied to the power spectrum produces a ~3σ shift in β_φ relative to other choices, so a systematic error budget is needed for DESI Y5.
  • The central value β_φ ≈ 2.7 maps to an unphysical N_eff if interpreted purely as a change in the number of neutrinos, meaning the standard-model interpretation is already strained; future data with σ(β) ~ 0.3 will decisively test whether the shift persists.

Reading between the lines

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

  • A natural next test is to fit β_φ with a flexible functional form for f(k) (varying k_* and ξ), because non-standard neutrino interactions are expected to change the scale dependence; if the high β_φ persists under such a flexible model, the case for new physics is much stronger.
  • The paper's result rests on the Planck prior for α and α_AP; a cross-check with a prior from a different dataset (e.g., CMB lensing or supernovae) would show whether the high β_φ is driven by the specific Planck chains used.
  • If the phase shift is indeed larger than standard-model neutrinos produce, the same effect should appear in the CMB's acoustic peaks; comparing with phase-shift constraints from the Planck CMB (e.g., Montefalcone et al. 2025) could reveal whether the discrepancy is a BAO-specific systematic or a genuine cosmological signal.
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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

4 major / 4 minor

Summary. This paper extends the Baumann et al. (2019) phase-shift methodology to anisotropic BAO fits, implements it in two independent public codes (desilike and Barry), validates the pipeline on first- and second-generation DESI mocks, and applies it to DESI DR1 data. The DESI-only combined constraint is beta_phi = 2.70 ± 1.70, and after importance-sampling the BAO posteriors with a Planck-based prior on the alpha and alpha_AP distortion parameters the paper quotes beta_phi = 2.7^{+0.60}_{-0.67}, interpreted as beta_phi > 0 at 4.3 sigma. The paper also identifies a ~3-sigma systematic difference in beta_phi between the polynomial power-spectrum broadband method and the other broadband/clustering choices, and it reports that the significance drops to 3.2-3.7 sigma when Alens, w, or w0-wa are varied.

Significance. If the 4.3-sigma detection were robust, it would be an interesting hint of physics beyond the standard-model Neff value, with implications for neutrino physics and BAO analyses. The paper's strengths include a careful, two-code mock validation program, public code release, tests of the fiducial/template cosmology dependence, and a transparent presentation of the individual tracer fits. The DESI-only measurement of beta_phi is a useful new result. However, the headline significance is not a DESI-only detection: it is driven by the Planck importance-sampling prior, it is not validated on mocks, and it is sensitive to the assumed cosmological model. The central claim therefore needs substantial reframing and additional quantification before the paper can be accepted.

major comments (4)
  1. [§4.1, Table 8, Eq. (29)] The headline 4.3-sigma significance is not a DESI-only measurement. As Table 8 shows, the DESI BAO-only combined fit gives beta_phi = 2.70 ± 1.70, i.e., only 1.6 sigma from zero. The tightened result beta_phi = 2.7^{+0.60}_{-0.67} comes entirely from importance-sampling the DESI posteriors with the Planck-based prior on alpha and alpha_AP in Eq. (29). Because that prior is constructed from Planck chains in which Neff is left free, and because alpha and alpha_AP are functions of r_s and the angular diameter distance (Eqs. 7 and 8), the prior implicitly carries Planck information on Neff through parameter correlations, despite the claim in §4.1 that 'we do not fold in any explicit CMB information on Neff.' This indirect injection should be quantified—for example by comparing with a prior derived from Planck chains with Neff fixed—and the importance-sampling procedure itself should be validated on the mock suite, since the current mock tests validate beta_phi recovery with beta free but not the Eq. (29) weighting step.
  2. [§3.1.4, Table 2] The paper reports a systematic difference in beta_phi of 0.29-0.40 (at 1.75-2.4 sigma, and up to 3 sigma when comparing the polynomial power-spectrum method to other methods) between broadband fitting methodologies, yet no systematic error is added to the quoted beta_phi uncertainty. The paper justifies this by noting the shift is smaller than the DESI DR1 statistical error and that the data results appear robust. However, the shift is comparable to the 0.6-0.7 uncertainty quoted for the Planck-prior combined result in Table 8, so it is not negligible for the central claim. The paper should either propagate this systematic into the final error budget or demonstrate quantitatively on the second-generation mocks and DR1 data that the final combined beta_phi constraint is insensitive to this choice for the specific pipelines used in the headline result.
  3. [§4.1, Table 8, Conclusions] The interpretation 'may hint at a phase shift that is not purely sourced from the standard model expectation for Neff' is model-dependent. Table 8 shows that the significance of beta_phi > 0 drops from 4.3 sigma in flat LCDM+Neff with w and Alens fixed to 3.7 sigma with Alens free, 3.4 sigma in wCDM, and 3.2 sigma in w0-waCDM, with the central value also moving from 2.70 to 2.05 in the Alens-free case. Since DESI DR1 itself moderately prefers the w0-waCDM model, the Planck-prior model choice is not neutral. The paper should present the DESI-only result as the primary measurement and clearly separate the model-dependent, prior-driven variants in the abstract, results, and conclusions, stating the full range of significances rather than only the 4.3-sigma value.
  4. [§2.3, Eqs. (17)-(18)] The analysis assumes the Baumann et al. functional form f(k) with fixed shape parameters (phi_inf, k*, xi). The mock validation only tests this shape for standard-model Neff variants (c000 and c003 cosmologies). If the true phase shift has a different k-dependence—for example from interacting neutrinos or non-adiabatic fluctuations, as the paper itself mentions in the conclusions—the fitted beta_phi will absorb the shape mismatch and the quoted amplitude constraint will be biased. The paper should make this limitation explicit in the abstract and, ideally, include a mock test with an alternative f(k) shape to quantify the bias in beta_phi.
minor comments (4)
  1. [Abstract] The abstract states the result 'relaxes in models with additional freedom beyond LCDM'; this caveat should be strengthened to explicitly state the model-dependent significance range (3.2-4.3 sigma) that is already present in Table 8, since the abstract's main numeric claim is the 4.3-sigma value.
  2. [§1 / Figure 1 caption] The caption 'This figure has been inspired by Figure 3 in Baumann et al. (2018)' is informal for a journal article; please rephrase to state that the figure reproduces or adapts the corresponding panel from that reference.
  3. [§4.1, footnote 13] The note that the alpha/alpha_AP prior is 'not the same as the prior included earlier from Planck on Neff' is confusing because the earlier validation in Section 4 also uses importance sampling with a Planck-based Neff prior. Clarify the distinction between the two uses of Planck chains.
  4. [Throughout] There are several typos and grammatical slips (e.g., 'used to to test' in §1, 'anistropic' in §2.2, and 'Baumman' in the Appendix A caption). A careful proofreading pass is recommended.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: beta_phi is a free amplitude fit to DESI BAO data; the f(k) template and Planck priors are external inputs, not derived from the target claim.

full rationale

The paper's central result is a measurement, not a derivation from its own conclusion. beta_phi is left free (prior U(-8,10), Table 5) and fitted to the BAO correlation functions; the DESI-only combined value beta_phi = 2.70 +/- 1.70 is quoted in Table 8. The headline 4.3-sigma significance is obtained by importance-sampling the BAO posteriors with Planck-based priors on alpha and alpha_AP (Eq. 29), which are external CMB data, not quantities constructed from the BAO phase-shift measurement itself. The mapping beta_phi -> Neff (Eq. 16) is a post-hoc interpretation, not an input to the fit. The f(k) shape (Eq. 17) is adopted from Baumann et al. (2018, 2019) with fixed constants (phi_inf = 0.227, k* = 0.0324, xi = 0.872) that do not depend on the fitted beta_phi or on the DESI data; it is a parameter-free template, and the paper validates recovery on c000 and c003 mocks. The fact that one present coauthor also appears on the cited Baumann et al. work is not load-bearing: the phase-shift phenomenon is independently established in Bashinsky & Seljak (2004), and the template is externally published and tested on mocks. The paper's own caveats about model dependence of the Planck prior, the unvalidated importance-sampling step on mocks, and the assumed functional form of f(k) are robustness or model-assumption concerns, not circular reductions. No equation in the paper is equivalent to its own output by construction, and no fitted parameter is renamed as a prediction.

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

The central measurement rests on the Baumann et al. phase-shift template, the DESI mock covariances, and the Planck importance-sampling prior. No new entities are introduced.

free parameters (4)
  • beta_phi = 2.7 ± 1.7 (DESI BAO alone); 2.7^{+0.60}_{-0.67} (with Planck prior)
    The phase shift amplitude is the target of the measurement and is fitted to the DESI BAO data.
  • BAO distortion parameters alpha, alpha_AP (or alpha_parallel, alpha_perp) = See Table 6, varies per tracer
    Geometric scaling parameters fitted along with beta_phi; they are degenerate with beta_phi, so their priors strongly affect the combined result.
  • Nuisance parameters: Sigma_s, Sigma_nl, b, f, broadband coefficients = Gaussian priors in Table 5; broadband coefficients free per polynomial/spline scheme
    Shape parameters of the BAO model; could shift beta_phi if priors are wrong or if the broadband model is misspecified.
  • Phase-shift shape parameters phi_inf, k*, xi = phi_inf=0.227, k*=0.0324 h/Mpc, xi=0.872 (fixed from Baumann et al. 2018)
    These coefficients define the scale dependence of the phase shift and are imported from prior theory fits; they are not refit here and are load-bearing for interpreting beta_phi.
assumptions (5)
  • domain assumption The BAO template model, Eq. (18), with the phase-shift parameterization of Baumann et al. (2018, 2019), correctly describes the observed power spectrum and correlation function.
    The measurement is defined relative to this template; if the model is wrong, beta_phi does not represent the physical phase shift.
  • domain assumption The template power spectrum is computed with CLASS at a Planck 2018 cosmology with Neff = 3.044; this defines the zero-point beta_phi = 1.
    The template cosmology sets the reference against which beta_phi is measured.
  • domain assumption The covariance matrices used (Hartlap-corrected mock covariances, RascalC, covaPT) are accurate estimates of the data covariance.
    Uncertainty on beta_phi and the reported significances depend on these covariances.
  • domain assumption The Planck 2018 chains used for importance sampling correctly represent the joint constraints on alpha and alpha_AP, and the importance-sampling product of per-tracer posteriors (Eq. 28) is a good approximation to the joint posterior.
    The headline 4.3 sigma detection is derived from this prior combination; the procedure is not validated on mocks.
  • standard math The relation beta_phi to Neff (Eq. 16) is used for the cosmological interpretation.
    Converts the measured phase shift amplitude to an effective number of relativistic species, assuming standard decoupling.

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Cite this review

Pith. "Pith review of Constraining the phase shift of relativistic species in DESI BAOs." pith.science (2026). https://pith.science/paper/RVGNYXMG

@misc{pith2026241205990,
  author       = {Pith},
  title        = {Pith review of: Constraining the phase shift of relativistic species in DESI BAOs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RVGNYXMG}},
  note         = {Machine review of arXiv:2412.05990}
}
abstract

In the early Universe, neutrinos decouple quickly from the primordial plasma and propagate without further interactions. The impact of free-streaming neutrinos is to create a temporal shift in the gravitational potential that impacts the acoustic waves known as baryon acoustic oscillations (BAOs), resulting in a non-linear spatial shift in the Fourier-space BAO signal. In this work, we make use of and extend upon an existing methodology to measure the phase shift amplitude $\beta_{\phi}$ and apply it to the DESI Data Release 1 (DR1) BAOs with an anisotropic BAO fitting pipeline. We validate the fitting methodology by testing the pipeline with two publicly available fitting codes applied to highly precise cubic box simulations and realistic simulations representative of the DESI DR1 data. We find further study towards the methods used in fitting the BAO signal will be necessary to ensure accurate constraints on $\beta_{\phi}$ in future DESI data releases. Using DESI DR1, we present individual measurements of the anisotropic BAO distortion parameters and the $\beta_{\phi}$ for the different tracers, and additionally a combined fit to $\beta_{\phi}$ resulting in $\beta_{\phi} = 2.7 \pm 1.7$. After including a prior on the distortion parameters from constraints using \textit{Planck} we find $\beta_{\phi} = 2.7^{+0.60}_{-0.67} $ suggesting $\beta_{\phi} > 0$ at 4.3$\sigma$ significance. This result may hint at a phase shift that is not purely sourced from the standard model expectation for $N_{\rm{eff}}$ or could be a upwards statistical fluctuation in the measured $\beta_{\phi}$; this result relaxes in models with additional freedom beyond $\Lambda$CDM.

Figures

Figures reproduced from arXiv: 2412.05990 by the authors.

Figure 1
Figure 1. This figure has been inspired by [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Top panel: the effect of altering 𝑁eff on the correlation function, calculated from a Fourier transform of the power spectrum shown in the top panel of [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Fits to the mean of 25 CV mocks using desilike and Barry for the correlation function. Here we show a comparison of the results both when 𝛽𝜙 is fixed or allowed to vary freely. The covariance matrix has been reduced by a factor of 25 compared to a single realization. We also consider the robustness of the fitting methodology in the case the true cosmology of the mocks has 𝑁eff set to a value that is not 𝑁eff = 3.044… view at source ↗
Figures from the paper (8 more)
Figure 5
Figure 5. Figure 5: Fits to the mean of 25 CV mocks using Barry, comparing spline and polynomial broadband methodologies. The covariance matrix has been reduced by a factor of 25 compared to a single realization. the parameters lies along their degeneracy direction and the fits are consis…
Figure 6
Figure 6. Figure 6: Similar to [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: Our fits of the 25 mocks and the mean for 𝛽𝜙 (top panel), 𝛼 (middle panel) and 𝛼AP (lower panel), for the 6 DESI samples considered here. The coloured points show desilike fits while the white points show the fits using Barry. Shaded regions show one standard deviation…
Figure 8
Figure 8. Figure 8: Our fits to 𝛽𝜙 from the combinations of the LRGs and ELGs (all tracer bins except QSOs and BGS) with the second-generation mocks, for desilike (black points) and Barry (white points). The shaded regions show the (weighted) 1-standard deviation about the weighted mean f…
Figure 9
Figure 9. Figure 9: Our fits to the DESI tracers in DR1. For ease of interpretation for the distortions to physical distances, we plot 𝛼∥ , 𝛼⊥ in place of 𝛼 and 𝛼𝐴𝑃 and additionally 𝛽𝜙. For BGS and QSOs we only study the isotropic scaling; as such we only plot 𝛼. MNRAS 000, 1–20 (2025) […
Figure 10
Figure 10. Figure 10: The best fit models for our the DESI tracers in the DR1 data with 𝛽𝜙 varying in the analysis, for comparison to the data. The coloured data shows the best fit models and data for the monopole, and the grey shows the quadrupole. The smaller panels show the isolated BAO…
Figure 11
Figure 11. Figure 11: Left panel: contours for 𝛼, 𝛼AP and 𝛽𝜙 for the baseline fits to the DESI DR1 data. The fits by QSOs and BGS which are not able to constrain 𝛽𝜙 well in the DR1 data are shown as dotted unfilled contours. Right panel: contours for Ωm, 𝑟𝑠ℎ (Mpc) for the baseline fits to …
Figure 12
Figure 12. Figure 12: Left panel: the 1D posterior fits for 𝛽𝜙, including a combined fit to the tracers (excluding BGS and QSOs, black dashed line), and various combined fits when a CMB prior for 𝛼 and 𝛼AP has been included by importance sampling (corresponding to the fits shown in [PITH_…

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Tracing the Neutrino-Induced Phase Shift in the 21-cm Spectrum

    astro-ph.CO 2025-09 conditional novelty 6.0 of 10

    The neutrino-induced phase shift in the 21-cm power spectrum is a redshift- and scale-dependent weighted average of two distinct templates: the known BAO phase shift and a newly computed, larger VAO phase shift.

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    write newline

    " write newline "" before.all 'output.state := FUNCTION fin.entry write newline FUNCTION new.block output.state before.all = 'skip after.block 'output.state := if FUNCTION new.sentence output.state after.block = 'skip output.state before.all = 'skip after.sentence 'output.stat...

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.