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Scalar-Tensor Gravity and DESI 2024 BAO data

T0 review · 5 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The Brans-Dicke Galileon model, fitted to Planck and DESI 2024 BAO data, puts $H_0$ at 71.0 and brings the SH0ES tension down to $1.2\sigma$.

desk verdict A competent, honest constraints paper whose BDG 'detection' is explicitly contingent on the two lowest DESI redshift bins; worth refereeing, not worth treating as a discovery yet. read the letter →

arxiv 2501.15298 v2 pith:GQPUIQKS submitted 2025-01-25 astro-ph.CO gr-qc

Angelo G. Ferrari , Mario Ballardini , Fabio Finelli , Daniela Paoletti This is my paper · ORCID
classification astro-ph.COgr-qc PACS 98.80.-k95.36.+x04.50.Kd
keywords scalar-tensorgravityBrans-DickeGalileonHubbletensionDESIBAObaryonacousticoscillationsmodifieddarkenergyequationofstatePlanckCMB
topics Dark EnergyThe Hubble Tension
open problems Dark EnergyThe 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 argues that the 2024 DESI baryon acoustic oscillation measurements, combined with Planck CMB data, favor scalar-tensor modifications of gravity over a cosmological constant. In the Brans-Dicke Galileon model the preferred value of the Galileon parameter is $1/e_{\alpha 8} = 0.255^{+0.095}_{-0.064}$, about $3\sigma$ away from the $\Lambda$CDM limit of zero, and the inferred Hubble constant rises to $H_0 = 71.0^{+1.5}_{-1.3}$ km/s/Mpc. At that value the long-standing $4.5\sigma$ disagreement between early- and late-universe $H_0$ measurements drops to $1.2\sigma$ with respect to the SH0ES local measurement. A sympathetic reader should care because, if the preference holds, a simple one-parameter extension of gravity can resolve the most prominent observational tension in cosmology while also producing the phantom dark-energy behavior that DESI has reported.

What carries the argument

The central object is the Brans-Dicke Galileon (BDG) model, a scalar-tensor theory with a nonminimal coupling $F(\sigma)R$, a negative kinetic term, and a Galileon term controlled by the parameter $\alpha$; the sampled combination is written as $1/e_{\alpha 8} = 10^{-8} e_\alpha$, with the $\Lambda$CDM limit at zero. In this theory the Galileon parameter is degenerate with the Hubble constant, so larger $1/e_{\alpha 8}$ pushes $H_0$ upward while leaving most other cosmological parameters close to their $\Lambda$CDM values. The model also relies on Vainshtein screening, which restores general relativity and the Newtonian gravitational constant on small scales while allowing the cosmological gravitational constant to evolve in time. The comparison models (induced gravity, $\Delta$IG, and EMG-CC) isolate which feature, nonminimal coupling versus a Galileon term, is responsible for the data preference.

What would settle it

Recompute the P18+DESI analysis using pre-reconstruction BAO distances or the linear-point estimator for the BGS and LRG1 bins; if the Galileon parameter $1/e_{\alpha 8}$ then becomes consistent with zero at below $2\sigma$, the claimed $3\sigma$ detection and the $1.2\sigma$ Hubble-tension reduction would be shown to depend on reconstruction systematics in those two bins.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that DESI 2024 BAO data break a previous degeneracy: the combination P18+DESI moves the Brans-Dicke Galileon parameter away from its $\Lambda$CDM value of zero, giving $1/e_{\alpha 8} = 0.255^{+0.095}_{-0.064}$ (68% CI, about $3\sigma$), and correspondingly raises $H_0$ to $71.0^{+1.5}_{-1.3}$ km/s/Mpc. The paper shows this is driven mainly by the first two DESI redshift bins (BGS and LRG1) and that the same mechanism operates in induced gravity, induced gravity with a gravitational-constant offset, and early modified gravity, all of which prefer larger modified-gravity parameters and higher $H_0$ with DESI than with previous SDSS BAO data. In BDG the fit improves over $\Lambda$CDM by $\Delta\chi^2 = -5.6$ ($\Delta\mathrm{AIC} = -3.6$), the dark-energy equation of state becomes phantom at low redshift, and the result sits between the SH0ES and CCHP local measurements, consistent with both.

Load-bearing premise

The central claim stands on the assumption that the DESI BAO measurements in the first two redshift bins (BGS and LRG1, $z<0.8$) are free of systematics that mimic a preference for higher $H_0$; replacing those bins with SDSS low-$z$ data lowers the Galileon parameter from $3\sigma$ to $2\sigma$ significance and raises the Hubble tension from $1.2\sigma$ to $2.6\sigma$.

Editorial extensions

If this is right

  • If the BDG preference is real, Planck and SH0ES measurements of $H_0$ agree at the $1.2\sigma$ level, so the Hubble tension does not require unknown systematics in either experiment.
  • The nonzero $1/e_{\alpha 8}$ value implies a dark-energy equation of state that crosses below $-1$ at low redshift, aligning with DESI's preference for dynamical dark energy over a pure cosmological constant.
  • Constraints on the nonminimal coupling $\xi$ in induced gravity become weaker with DESI than with SDSS because DESI pulls $H_0$ higher, changing the upper limits cosmology can place on modified-gravity parameters.
  • Replacing the two lowest DESI redshift bins with SDSS low-$z$ data reduces the Galileon significance from $3\sigma$ to $2\sigma$ and raises the $H_0$ tension to $2.6\sigma$, showing that the result depends on those specific bins.
  • When a SH0ES prior is added, BDG improves over $\Lambda$CDM by $\Delta\chi^2 = -23.4$ and $\Delta\mathrm{AIC} = -21.4$, making the model statistically preferred when local $H_0$ information is included.

Reading between the lines

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

  • If the $3\sigma$ detection survives scrutiny of the low-redshift DESI bins, a next testable signature is the predicted present-day time variation of the gravitational constant, $\dot{G}_{\rm cosm}/G_{\rm cosm} \simeq -1.1 \times 10^{-12}$ yr$^{-1}$, which improved lunar laser ranging or solar-system ephemerides could detect or rule out.
  • The paper's own dataset substitution suggests a decisive cross-check: reanalyzing with pre-reconstruction BAO estimators or the linear-point method in the BGS and LRG1 bins should either confirm or erase the $1/e_{\alpha 8}$ detection.
  • Because only BDG among the four models generates a phantom equation of state, the comparison implies that the Galileon term, not the nonminimal coupling per se, is what makes the fit to DESI BAO data work; models without that term only mildly ease the tension.
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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

5 major / 4 minor

Summary. The paper analyzes four scalar-tensor gravity models (induced gravity IG, induced gravity with an effective gravitational-constant imbalance DeltaIG, Brans-Dicke Galileon BDG, and early modified gravity with conformal coupling EMG-CC) against Planck 2018 CMB data combined with DESI 2024 BAO data, with variants replacing the two lowest DESI redshift bins by SDSS low-z BAO data and with SH0ES/CCHP H0 priors. The main claim is that BDG prefers a nonzero Galileon term, 1/eα8 = 0.255+0.095−0.064, about 3σ from the ΛCDM limit, and H0 = 71.0+1.5−1.3 km/s/Mpc, reducing the SH0ES tension to 1.2σ, while the same parameter is only an upper limit with previous SDSS BAO data. The paper also reports that this preference is mainly driven by the first two DESI redshift bins, and that replacing them with SDSS data lowers the Galileon significance to roughly 2σ and increases the H0 tension to 2.6σ. The IG, DeltaIG, and EMG-CC models do not show a statistical preference over ΛCDM with CMB+BAO alone.

Significance. If the BDG detection were robust, this would be an interesting and timely result: a concrete modified-gravity model that simultaneously explains the DESI BAO preference for dynamical dark energy and substantially alleviates the Hubble tension, with a full treatment of background and perturbations rather than a phenomenological parametrization. The authors are to be credited for performing a complete Einstein-Boltzmann treatment, for comparing four models on equal footing, and for explicitly reporting the cross-check with SDSS low-z data instead of hiding the fragility. However, the central claim is highly sensitive to the low-redshift DESI bins, and the paper contains internal inconsistencies in the reported significance and in the treatment of lunar laser ranging constraints. The significance for the field is therefore conditional: the manuscript is a useful parameter study, but its headline conclusion needs additional robustness work before it can be regarded as a secure detection.

major comments (5)
  1. [Abstract; Section IV.B; Table III] The headline BDG detection is not robust to the choice of low-z BAO data. With P18+DESI the Galileon parameter is 1/eα8 = 0.255+0.095−0.064 and H0 = 71.0+1.5−1.3, but with P18+(DESI+SDSS), which replaces the BGS and first LRG bins with SDSS low-z data, the same parameter becomes 0.157+0.088−0.076 (consistent with zero at about 2σ) and H0 = 69.2+0.9−1.2, with the SH0ES tension growing to 2.6σ. Since the abstract itself states that the results are 'mainly driven by the first two redshift bins of DESI,' the central claim is contingent on those two bins being free of systematics. The authors should either provide an explicit systematic-robustness analysis of the BGS and LRG1 measurements, or substantially rephrase the conclusions to present the BDG preference as dataset-dependent rather than as a detection.
  2. [Section IV.B, Eq. following 'about 3σ'] The claim that 1/eα8 = 0.255+0.095−0.064 is 'about 3σ away from the ΛCDM value of 0' is not supported by the quoted asymmetric 68% interval alone: the ratio of the mean to the two one-sided errors gives values between about 2.7 and 4.0, and for a strongly non-Gaussian posterior either number is not a valid significance. The authors should report the posterior probability at zero, or the credible interval excluding zero, to justify the significance statement. This is load-bearing because the '3σ detection' is the paper's central quantitative result.
  3. [Section IV.B, Gdot/Gcosm paragraph; Table III] The quoted time derivative of the cosmological gravitational constant for P18+DESI, Gdot/Gcosm(z=0) = (−11.1+2.4−3.9)×10^-13 yr^-1, does not contain zero at even the 2σ level under a Gaussian interpretation, and the same is true for the P18+(DESI+SDSS) value (−7.1+3.1−3.9)×10^-13. The sentence that these values are 'consistent with 0 at the 2σ level' is therefore inaccurate. The subsequent arguments that LLR constraints may be weakened by core-rotation correlations or by inhomogeneous local evolution are plausible directions but are not quantified here. As written, the paper simultaneously acknowledges exceeding the LLR limits and asserts consistency with zero, which is internally inconsistent and leaves the viability of BDG unclear.
  4. [Section III.B (BDG sampling)] In the BDG analysis the nonminimal coupling is fixed to ξ = 5×10^-5 rather than sampled, and only the Galileon amplitude 1/eα8 varies. Since the posterior for 1/eα8 is strongly degenerate with H0 and the model's viability depends on the chosen ξ, the reported 'detection' is conditional on an untested prior choice. A robustness check varying ξ within a range consistent with solar-system and cosmological constraints, or a discussion of why the result is insensitive to ξ, is needed before the 3σ claim can be taken as a property of the model class rather than of the chosen parameter point.
  5. [Table IV vs Section IV.D.3] There is a numerical inconsistency in the EMG-CC results: the text states that with P18+DESI+SH0ES the 95% upper bound is 'V0 < 1.2,' while Table IV reports 'V0 < −1.2 (95%)'. The same table also uses an em-dash for the other dataset combinations, so the reader cannot tell which value is correct. In addition, the Conclusions section contains an incomplete sentence 'Δχ2 = − for EMG-CC' with a missing number. These need to be corrected.
minor comments (4)
  1. [Section IV.C] The text says 'the 65% CI for the Hubble constant' where the context and tables indicate a 68% credible interval.
  2. [Section III (datasets)] The paper would be easier to reproduce if the chains or the modified CLASSig likelihood code were made public, or if a link to the existing public code were provided. The current reference list names Cobaya and CLASS, but not the exact version or repository used for the modified gravity extension.
  3. [Figure 2 and Appendix C] The definition of wDE in Eq. (C12) is clear, but the comparison with the w0waCDM curve in Figure 2 would benefit from a statement about how the latter is normalized (e.g., whether it is evaluated at the same best-fit background) and from error bars on the wDE curve, since the differences between models are otherwise hard to assess.
  4. [Section IV.B, previous constraint] The statement that DESI constrains 1/eα8 'by a factor of 2 better' than the earlier SDSS upper limit is imprecise; the earlier work gave an upper limit, not a measurement, so a direct comparison of precision is not straightforward. Please clarify what is meant.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the BDG Galileon parameter and H0 are posterior outputs of standard MCMC on external Planck and DESI data, not re-labeled inputs or self-citation-derived predictions.

full rationale

The paper performs conventional Bayesian parameter estimation: cosmological parameters including H0 and the modified-gravity parameter 1/eα8 are sampled, with the likelihood built from externally published Planck and DESI/SDSS measurements. There is no equation in which a claimed prediction is defined in terms of the data that it purportedly predicts: the 3σ departure of 1/eα8 from zero and the H0 = 71.0 posterior are outputs of the P18+DESI analysis, not inputs. The boundary conditions fixing Geff or Gcosm to measured values are physical consistency constraints imported from solar-system physics, not fitted predictions. The main self-citations are to the authors' earlier model implementations and priors (e.g., CLASSig in Ref. [77] and the fixed ξ = 5×10−5 in Ref. [87]); these are code and model-prescription reuse, and the central inference remains sensitive to external data rather than being forced by those citations. The paper's own limitation statement that the result is 'mainly driven by the first two redshift bins of DESI' and the DESI+SDSS cross-check showing reduced significance are empirical robustness concerns, not circularity: replacing data changes the posterior, which is exactly what a non-circular inference should do. No fitted quantity is renamed as a prediction, no uniqueness theorem from the authors' prior work is invoked to forbid alternatives, and no derived result reduces by construction to its own input. Therefore the circularity score is 0.

Assumptions & free parameters 6 free parameters · 4 assumptions · 0 invented entities

The central BDG claim rests on the sampled Galileon amplitude 1/eα8 and the hand-fixed nonminimal coupling ξ, plus standard cosmological parameters not itemized here. The key axioms are the Horndeski action form, Vainshtein screening, the homogeneous-field assumption for local Gdot, and the reliability of the low-z DESI bins. No new entities are introduced.

free parameters (6)
  • 1/eα8 (BDG Galileon amplitude) = 0.255+0.095-0.064 (68% CI, P18+DESI)
    Sampled in [0, 0.4]; the posterior is about 3σ from 0, driving the H0 shift.
  • ξ (BDG nonminimal coupling) = 5e-5 (fixed by hand)
    Fixed, following Ref [87], to a value too large for Solar System tests absent screening; the model's cosmological behavior depends on it.
  • ζIG (IG and ∆IG coupling) = < 0.0035 (95% CI, P18+DESI)
    Sampled in [0, 0.039]; the DESI data relax the constraint relative to pre-DESI BAO.
  • ∆ (∆IG gravitational-constant imbalance) = -0.008 ± 0.035 (P18+DESI)
    Sampled in [-0.3, 0.3]; consistent with zero.
  • σini/MPl (EMG-CC initial field) = < 0.38 (95% CI, P18+DESI)
    Sampled in [0, 0.9]; constrained as an upper limit.
  • V0 (EMG-CC potential amplitude) = unconstrained (P18+DESI)
    Sampled in [-4, 3.5]; only constrained with the SH0ES prior (V0 < 1.2, 95% CI, per text).
assumptions (4)
  • domain assumption The action (1) with the specified Horndeski functions (2) captures the relevant gravitational physics on cosmological scales.
    All models are subclasses of Horndeski gravity; the paper assumes these are viable descriptions of dark energy and modified gravity.
  • domain assumption Vainshtein screening suppresses the scalar field's local effects in BDG, so the model passes Solar System tests and the local gravitational constant is Gcosm.
    Section II model (iii) invokes Vainshtein screening (Refs [109, 110]) to evade Solar System bounds; this is standard but not derived in the paper.
  • ad hoc to paper The homogeneous cosmic evolution of the scalar field can be used to compute the local time derivative of the gravitational constant, comparable to LLR bounds.
    Section IV B states the LLR comparison assumes homogeneous local evolution and notes that inhomogeneous evolution could suppress the local variation, weakening the constraint.
  • domain assumption The DESI BAO likelihood and the first two redshift bins are free of systematics that mimic a preference for higher H0.
    The paper's headline result is driven by the first two DESI bins; replacing them with SDSS data reduces the Galileon preference from 3σ to 2σ (Section IV B).

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Cite this review

Pith. "Pith review of Scalar-Tensor Gravity and DESI 2024 BAO data." pith.science (2026). https://pith.science/paper/GQPUIQKS

@misc{pith2026250115298,
  author       = {Pith},
  title        = {Pith review of: Scalar-Tensor Gravity and DESI 2024 BAO data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GQPUIQKS}},
  note         = {Machine review of arXiv:2501.15298}
}
abstract

We discuss the implications of the DESI 2024 BAO data on scalar-tensor models of gravity. We consider four representative models: induced gravity (IG, equivalent to Jordan-Brans-Dicke), where we either fix today's value of the effective gravitational constant on cosmological scales to the Newton's constant or allow them to differ, Jordan-Brans-Dicke supplemented with a Galileon term (BDG), and early modified gravity (EMG) with a conformal coupling. In this way it is possible to investigate how different modified gravity models compare with each other when confronted with DESI 2024 BAO data. Compared to previous analyses, for all of these models, the combination of Planck and DESI data favors a larger value of the key parameter of the theory, such as the nonminimal coupling to gravity or the Galileon term, leading also to a larger value of $H_0$, due to the known degeneracy between these parameters. These new results are mainly driven by the first two redshift bins of DESI. In BDG, in which we find the largest value for $H_0$ among the models considered, the combination of Planck and DESI is consistent with CCHP results and reduces the $H_0$ tension with the SH0ES measurement to $1.2\sigma$ (compared to $4.5\sigma$ of $\Lambda$CDM in our Planck + DESI analysis).

Figures

Figures reproduced from arXiv: 2501.15298 by the authors.

Figure 1
Figure 1. FIG. 1. BAO distance scales measured by the DESI Collab [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The equation of state parameter for dark-energy com [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Marginalized 68% and 95% 2D credible regions comparing P18+DESI and P18+(DESI+SDSS) datasets for the IG [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Marginalized 68% and 95% 2D credible regions comparing P18+DESI and P18+(DESI+SDSS) datasets for the ∆IG [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Marginalized 68% and 95% 2D credible regions comparing P18+DESI and P18+(DESI+SDSS) datasets for the BDG [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. SH0ES and CCHP local measurements of the Hub [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Marginalized 68% and 95% 2D credible regions comparing P18+DESI and P18+(DESI+SDSS) datasets for the EMG [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Marginalized 68% and 95% 2D credible regions [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Triangle plot in IG comparing results for P18+SDSS, P18+DESI, P18+(DESI+SDSS), P18+DESI+SH0ES, and [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Triangle plot in ∆IG comparing results for P18+SDSS, P18+DESI, P18+(DESI+SDSS), P18+DESI+SH0ES, and [PITH_FULL_IMAGE:figures/full_fig_p015_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11. Triangle plot in BDG comparing results for P18+SDSS, P18+DESI, P18+(DESI+SDSS), P18+DESI+SH0ES, and [PITH_FULL_IMAGE:figures/full_fig_p016_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12. Triangle plot in EMG-CC comparing results for P18+DESI, P18+(DESI+SDSS), P18+DESI+SH0ES, and [PITH_FULL_IMAGE:figures/full_fig_p017_12.png]

Discussion (0). Continue with ORCID to comment.

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