Brans-Dicke gravity with a cosmological constant smoothes out $\Lambda$CDM tensions

Adria Gomez-Valent; Cristian Moreno-Pulido; Javier de Cruz Perez; Joan Sola

REVIEW 4 major objections 4 minor 6 cited by

Brans-Dicke gravity with a cosmological constant smoothes out $\Lambda$CDM tensions

T0 review · 4 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A Brans-Dicke gravity model with a bare cosmological constant and no extra dark energy fluid fits the combined cosmological data better than GR-based ΛCDM and dissolves the H0 and σ8 tensions.

desk verdict A technically solid BD-LCDM fit that softens H0 and sigma8 tensions, but its viability leans on an unproven screening assumption that lets |omega_BD|~300 evade Cassini bounds; deserves a real referee. read the letter →

arxiv 1909.02554 v3 pith:2JJZWK4Y submitted 2019-09-05 astro-ph.CO gr-qchep-ph

Joan Sola , Adria Gomez-Valent , Javier de Cruz Perez , Cristian Moreno-Pulido This is my paper · ORCID

classification astro-ph.COgr-qchep-ph PACS 98.80.-k04.50.Kd

keywords Brans-DickegravitycosmologicalconstantHubbletensionsigma8effectivedarkenergyequationofstatequintessencemodifiedparameterestimation

topics Dark Energy The Hubble Tension

open problems Dark Energy

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 standard cosmological model's two most persistent headaches — the higher local value of the Hubble constant and the surplus structure-growth amplitude — both relax when gravity is described by Brans-Dicke theory with a bare cosmological constant and cold dark matter (BD-ΛCDM). Fitting supernova, H(z), BAO, redshift-space-distortion, weak-lensing, and full Planck 2015 CMB data, the model is preferred over the general-relativistic ΛCDM by standard information criteria. The best fit raises H0 from about 68.6 to 71–72 km/s/Mpc, cutting the tension with local distance-ladder measurements to about 1–2σ, while σ8 stays near 0.80. From the GR viewpoint the extra degrees of freedom look like a dynamical dark energy component whose equation of state is quintessence-like ($w_{\rm eff}(0)\simeq -0.96$) at above 3σ significance near the present epoch. If right, no new dark energy fluid is needed: a mildly time-varying gravitational coupling and the cosmological constant suffice to smooth out both tensions.

What carries the argument

The carrying object is the dimensionless Brans-Dicke field $\phi(t)=G_N/G(t)$, with $\epsilon_{\rm BD}=1/\omega_{\rm BD}$ measuring the departure from GR. Rewriting the BD field equations as Friedmann equations produces an effective BD-fluid energy density and pressure, whose combined equation of state with the vacuum term is $w_{\rm eff}(t)$; near $z=0$ this takes the approximate form $w_{\rm eff}\simeq -1 + \frac{\Delta\phi\,\Omega_{m0}}{1-\Omega_{m0}}(1+z)^3$. On the perturbation side, the linear matter-density contrast obeys a modified growth equation in which the effective gravitational constant is $(G_N/\phi)(2+4\epsilon_{\rm BD})/(2+3\epsilon_{\rm BD})$. These two pieces — background equation of state and growth equation — let a single parameter $\epsilon_{\rm BD}$ shift both $H_0$ and $\sigma_8$ in the observed directions.

What would settle it

A cosmological-scale constraint that forced $|\omega_{\rm BD}|\gtrsim10^4$ at all epochs, or a null measurement of $\dot G/G$ at the level of $10^{-14}\,\mathrm{yr}^{-1}$, would exclude the fitted $\epsilon_{\rm BD}\simeq -0.003$ and remove the claimed tension relief.

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Extended reading notes

Core claim

The central claim is that BD-ΛCDM — Brans-Dicke gravity with a constant vacuum term and no interaction between the scalar field and matter — provides a better fit to the combined cosmological dataset than the GR-based ΛCDM, with the H0 and σ8 tensions essentially disappearing. In the best fit, $\epsilon_{\rm BD}\simeq -0.003$ (i.e. $\omega_{\rm BD}\simeq -300$), $\phi(0)\simeq 0.90$, so G is slightly larger and growing at present, $\dot G/G\simeq +3\times10^{-13}\,\mathrm{yr}^{-1}$. The model yields $H_0\simeq 71$–$72\,\mathrm{km\,s^{-1}\,Mpc^{-1}}$, in line with the local distance ladder at the 1–2σ level, and $\sigma_8\simeq 0.80$, in between Planck and weak-lensing values. In the GR frame the BD field contributes an effective dark-energy fluid with a time-varying equation of state that near $z=0$ takes $w_{\rm eff}\simeq -0.96$, mimicking quintessence at more than 3σ. The DIC and AIC differences between the models lie between 5 and 10, which the authors read as strong evidence for BD-ΛCDM.

Load-bearing premise

The whole fit rests on assuming the Solar System bound on the Brans-Dicke parameter, $|\omega_{\rm BD}|>40000$, does not apply at cosmological scales, allowing $|\omega_{\rm BD}|\simeq 300$ through screening.

Editorial extensions

If this is right

The tension with the local distance-ladder value of $H_0$ drops from about 4.4σ in ΛCDM to roughly $1.8\sigma$ (DS1) and $1.1\sigma$ (DS2).
The mass-fluctuation amplitude stays at $\sigma_8\simeq 0.80$, sitting between the higher Planck value and the lower cosmic-shear value and thereby easing the $\sigma_8$ tension.
Near the present epoch the effective dark energy equation of state is $w_{\rm eff}\simeq -0.96$, a quintessence-like signal at $\gtrsim 3\sigma$, which the authors describe as a smoking gun of the underlying BD dynamics.
The model is favored over ΛCDM by both DIC and AIC with differences between 5 and 10, which standard model-selection practice treats as strong evidence.
The fitted value of the Brans-Dicke parameter, $|\omega_{\rm BD}|\simeq 300$, keeps the model close enough to GR to be phenomenological while predicting a mild, positive present-day time variation of $G$.

Reading between the lines

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

The paper leaves implicit that the same scalar field can in principle absorb both tensions at once, which suggests a common physical origin — a mildly running gravitational coupling — rather than two independent systematics.
If the model is right, future BAO and weak-lensing surveys should see the effective dark energy equation of state deviate from $-1$ at low redshift in the direction of quintessence, with the deviation growing roughly as $(1+z)^3$.
A null detection of the predicted present-day growth of $G$, $\dot G/G\simeq 3\times10^{-13}\,\mathrm{yr}^{-1}$, with upcoming lunar-laser-ranging or atomic-clock experiments would put the model under direct observational pressure.
The screening assumption could be tested cross-model: if the cosmological Brans-Dicke parameter really is as small as $|\omega_{\rm BD}|\simeq 300$, comparable tension relief should appear in other screened modified-gravity theories fitted to the same 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.

Desk Editor's Note

read the letter

Quick take: this is a competent, well-documented full-data fit of BD-LCDM, and it does soften the H0 and sigma8 tensions with a moderate DIC/AIC preference over LCDM. But the model's fitted |omega_BD| about 300 is only viable if solar-system bounds are switched off, and the paper has no screening mechanism to justify that switch. Treat it as a phenomenological cosmology paper, not as a resolution of the tensions.

What is actually new: earlier papers from this group used approximate power-law solutions; this one solves the background and perturbation equations exactly and runs them against the full Planck 2015 likelihood together with SnIa, BAO, RSD, WL, and R19. That is a real step. The perturbation equation (quoted from Boisseau et al.) reduces to LCDM in the GR limit, the MCMC and model-selection tools are public and standard, and the residual H0 tension (1.1-1.8 sigma) and sigma8 about 0.80 are reported honestly.

Soft spots in proportion. The biggest is explicitly acknowledged in Section 3: the authors 'take the wider perspective' that cosmological BD is not restricted by astrophysical-neighborhood bounds, citing screening. But the action they use has no scalar potential and no self-interactions; the BD field is massless. In the static weak-field limit the same theory gives gamma-1 about 3e-3 at the fitted epsilon_BD, two orders of magnitude above Cassini. So the screened escape route is an assumption, not a property of the model they wrote down. A referee should ask for the screening sector or a citation to a concrete mechanism in this exact model.

Second, the 'quintessence at more than 3 sigma' claim is a reparametrization of the fitted BD field parameters, not an independent detection. The significance inherits from the same chain that fixed epsilon_BD and phi_ini. It is a nice interpretive frame, not a new observable.

Third, the perturbation equation is quoted without derivation, with details deferred to a future paper. Acceptable in a letter, but a serious referee should want the calculation or a fuller reference.

Fourth, because R19 is in the dataset, the reduced H0 tension is partly by construction. The model is flexible enough to pull H0 up while keeping sigma8 low; that is the real result, stated without overclaiming.

Who this is for: modified-gravity and tension people. I would bring it to our reading group, and I would cite the exact numerical treatment if I worked in BD cosmology. The screening issue does not kill the paper as a statistical/physical analysis, but it prevents using the result as evidence for BD gravity at cosmological scales without additional physics. Deserves a serious referee; I would send it out, with the screening point pressed.

Referee Report

4 major / 4 minor

Summary. The manuscript analyzes Brans-Dicke gravity with a bare cosmological constant and cold dark matter (BD-ΛCDM) against a combination of SnIa, H(z), BAO, RSD, weak lensing, and the full Planck 2015 CMB likelihood. The authors use two data sets, DS1 and DS2, with the public codes CLASS and MontePython, fitting eight parameters including the BD parameters ε_BD and φ_ini. They report that BD-ΛCDM is preferred over GR-based ΛCDM by ΔDIC ≈ 8.3–9.9 and ΔAIC ≈ 7.7–9.9, with H0 ≈ 71–72 km/s/Mpc, σ8 ≈ 0.80, and an effective dark-energy equation of state w_eff(0) ≈ −0.95 to −0.96, which they interpret as quintessence-like behavior at ≳3σ. The paper concludes that the H0 and σ8 tensions of ΛCDM essentially disappear in this context. The central load-bearing elements are the quoted matter-perturbation equation, the screening assumption that bypasses solar-system bounds on ω_BD, and the interpretation of the fitted BD field as an effective quintessence component.

Significance. If the central claim holds, BD-ΛCDM would be a minimal and economical modification of the concordance model that resolves two major tensions without introducing a new dark-energy fluid. The paper's strengths are its use of standard public pipelines and the full Planck 2015 likelihood, the explicit reporting of marginalized constraints and information-criterion differences, and a clear statement of the screening assumption. These features make the statistical comparison reproducible in principle. However, the quoted growth equation is not derived, the screening mechanism is not specified, and the quintessence signal is a reparameterization of the fitted BD field rather than an independent observable. As a result, the confidence that can currently be placed in the model-selection preference is limited, and the interpretation of the 3σ w_eff result needs to be framed more carefully.

major comments (4)

[§3, Eq. (10)] The linear matter-perturbation equation is quoted without derivation, with the details deferred to a future 'more complete presentation.' Equation (10) is the basis for the reported σ8, RSD, WL, and bispectrum fits, so the central model-selection result depends on it. Please provide a derivation or a public implementation that demonstrates how the modified CLASS equations reproduce Eq. (10) in the subhorizon limit, including the treatment of the BD scalar-field perturbations and the (2+4ε)/(2+3ε) coupling factor. As written, the growth sector cannot be independently verified.
[§3, screening of solar-system bounds] The fitted value ε_BD ≈ −0.003 corresponds to |ω_BD| ≈ 300 and to a PPN parameter γ−1 ≈ 3×10^−3, which is more than two orders of magnitude above the Cassini bound. The manuscript explicitly sets aside local bounds and appeals to screening, but the action in §2 contains no potential for ψ, no nonlinear self-interactions, and no chameleon, Vainshtein, or symmetron mechanism that would make ω_BD environment-dependent. The manuscript should either specify a concrete screening mechanism that reconciles the cosmological and local values, or present the analysis as conditional on this assumption and quantify how severely the Cassini bound would restrict the fitted region if it applies.
[§2.2, Eq. (8) and §4.2, w_eff(0)] The claim that BD-ΛCDM 'mimics quintessence at more than 3σ' is a restatement of the fitted BD field, not an independent constraint: w_eff is constructed from the same fitted φ that enters the background and growth equations, so the 3σ deviation from −1 is a derived parameter rather than a new observable. In addition, the functions f1 and f2 in Eq. (8) are not given explicitly, and the statement that they are 'numerically negligible' is asserted without a bound. Please provide explicit expressions and a quantitative assessment of the dropped terms near z = 0, and describe the reported significance as a constraint on the derived w_eff rather than as an independent detection of quintessence.
[§4.2, initial conditions] The numerical solution fixes φ'(z_ini) = 0 at z_ini = 10^14. This is a nontrivial theoretical input: the BD scalar is dynamical, and imposing a zero initial velocity at a finite initial epoch is a prior on the solution space. The paper reports no test of the sensitivity of H0, σ8, or ΔDIC/ΔAIC to the choice of z_ini and to the initial derivative. Please add a convergence/sensitivity test (for example, varying z_ini by an order of magnitude and allowing a non-zero initial derivative) to show that the model-selection result is not driven by this boundary condition.

minor comments (4)

[§2.1, before Eq. (4)] There is a typo, 'Hearafter', that should read 'Hereafter'.
[§2.2, Eq. (8)] The sentence 'The two functions f1,2 need not be specified here' is unsatisfactory in a Letter whose central claim is based on w_eff; at minimum, the explicit expressions should be given in an appendix or in a companion public file.
[§4.2 and Table 1] The compressed notation for the 1σ, 2σ, and 3σ intervals in the Table 1 caption is difficult to parse; please present the 68% intervals in the main table and move the extended intervals to a supplementary table.
[References] The Hildebrandt et al. entry is given only as an arXiv number; please add the journal reference if published.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: model comparison is data-driven, and the 'quintessence-like' EoS is a reparameterization of the fitted scalar field rather than a circular derivation.

full rationale

The paper's central claim is a cosmological model comparison performed with CLASS and MontePython against external datasets (SnIa, H(z), BAO, RSD, weak lensing, and Planck 2015 CMB). The fitted values of H0, sigma8, epsilon_BD, and phi_ini are genuinely constrained by these data, and the DIC/AIC preference for BD-LambdaCDM is a standard model-selection result, not a quantity identical by construction to an input. The statement that BD-LambdaCDM 'mimics quintessence at more than 3 sigma' is a postdiction: Eq. (8) defines w_eff directly from the fitted BD field phi and its derivatives, so the reported quintessence signal inherits the fitted phi_ini rather than being an independent first-principles prediction. This is ordinary parameter inference, not a circular reduction of the kind in which a fitted parameter is renamed as a predicted observable. There are minor self-citations (e.g., 'Both features are consistent with previous estimates from analytical power-law solutions found in Sola (2018) and de Cruz Perez & Sola (2018)') and a data-description citation to the same group's 2019 paper, but these are not load-bearing: the numerical fit and the external perturbation equation (Eq. 10, cited to Boisseau et al. 2000) carry the argument. The paper's explicit assumption that solar-system bounds on omega_BD need not apply at cosmological scales ('we take the wider perspective that the BD theory, when applied to the cosmological level, is not restricted by the bounds obtained in the astrophysical neighborhood') is a physical/correctness risk about screening, not a circularity. The deferred perturbation derivation is an omission, not a circular step. Overall, no derivation step reduces to its own input by construction; the modest score reflects the minor self-citations and the fact that the quintessence signal is a fitted-output reparameterization rather than a true prediction.

Assumptions & free parameters 8 free parameters · 6 assumptions · 0 invented entities

The paper's model adds two fitted parameters to the standard six: epsilon_BD and phi_ini. The Brans-Dicke scalar field is not new to this paper. The two load-bearing assumptions are the quoted perturbation equation and the cosmological-scale freedom of omega_BD from solar-system bounds.

free parameters (8)

H0 = 68.65 to 72.00 km/s/Mpc across fits
Hubble constant today, standard free parameter in both LambdaCDM and BD-LambdaCDM fits; the claimed H0 tension relief depends on it.
Omega_m0 = 0.2665 to 0.2955
Total nonrelativistic matter density parameter today, standard free parameter.
Omega_b0 = 0.0443 to 0.0476
Baryon density parameter, standard free parameter.
tau = 0.063 to 0.084
Reionization optical depth, standard free parameter.
n_s = 0.9700 to 0.9945
Primordial spectral index, standard free parameter.
sigma8(0) = 0.801 to 0.804
Amplitude of matter fluctuations today; the BD fit keeps it near 0.80, which helps the sigma8 tension claim.
epsilon_BD = -0.00277 +0.00170 -0.00154 (DS1); -0.00315 +0.00168 -0.00175 (DS2)
Inverse Brans-Dicke parameter, fitted to data; small negative value gives |omega_BD| around 300, the key deviation from general relativity.
phi_ini = 0.924 +0.021 -0.023 (DS1); 0.901 +0.026 -0.025 (DS2)
Initial value of the dimensionless Brans-Dicke field at z=10^14; together with epsilon_BD it sets the present field phi(0) around 0.90 and the effective quintessence deviation Delta_phi > 0.

assumptions (6)

domain assumption BD field equations (1)-(3) with no potential for the scalar and with a fundamental cosmological constant Lambda
Defines the theory being tested; assumes Lambda is a bare constant and there is no direct interaction between matter and the Brans-Dicke field.
domain assumption Flat FLRW metric
Assumes spatial flatness; the field equations are solved on this background, standard in such analyses.
domain assumption Separate conservation of baryons, cold dark matter, photons and neutrinos
Follows from no direct coupling between matter and psi; used to evolve background densities.
domain assumption Subhorizon perturbation equation (10) from Boisseau et al. 2000
The growth equation is quoted rather than derived; the LSS likelihood depends on it.
ad hoc to paper Solar-system bounds on omega_BD can be screened at cosmological scales
Allows fitted |omega_BD| around 300 despite local limits; if this fails, the model is immediately ruled out.
ad hoc to paper Initial derivative of phi is zero at z_ini = 10^14
A boundary condition chosen for convenience; the mild evolution claimed depends on this initial condition.

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Pith. "Pith review of Brans-Dicke gravity with a cosmological constant smoothes out $\Lambda$CDM tensions." pith.science (2026). https://pith.science/paper/2JJZWK4Y

@misc{pith2026190902554,
  author       = {Pith},
  title        = {Pith review of: Brans-Dicke gravity with a cosmological constant smoothes out $\Lambda$CDM tensions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2JJZWK4Y}},
  note         = {Machine review of arXiv:1909.02554}
}

abstract

We analyze Brans-Dicke gravity with a cosmological constant, $\Lambda$, and cold dark matter (BD-$\Lambda$CDM for short) in the light of the latest cosmological observations on distant supernovae, Hubble rate measurements at different redshifts, baryonic acoustic oscillations, large scale structure formation data, gravitational weak-lensing and the cosmic microwave background under full Planck 2015 CMB likelihood. Our analysis includes both the background and perturbations equations. We find that BD-$\Lambda$CDM is observationally favored as compared to the concordance $\Lambda$CDM model, which is traditionally defined within General Relativity (GR). In particular, some well-known persisting tensions of the $\Lambda$CDM with the data, such as the excess in the mass fluctuation amplitude $\sigma_8$ and specially the acute $H_0$-tension with the local measurements, essentially disappear in this context. Furthermore, viewed from the GR standpoint, BD-$\Lambda$CDM cosmology mimics quintessence at $\gtrsim3\sigma$ c.l. near our time.

Figures

Figures reproduced from arXiv: 1909.02554 by the authors.

**Figure 1.** Triangular matrix containing some relevant combinations of two-dimensional marginalized distributions for fitting parameters of the BD model (at 1σ, 2σ and 3σ c.l.), together with the corresponding one-dimensional marginalized likelihoods for each parameter. H0 is expressed in km/s/Mpc. We present the contours for the data sets DS1 (in purple) and DS2 (in red) (cf [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗

**Figure 2.** The effective EoS parameter for the BD model and its corresponding 1σ bands as a function of the redshift, Eq. (8). We plot the results derived under both, dataset DS1 (in purple) and DS2 (in red), in the redshift range z < 106 . In black we plot the EoS parameter of the vacuum energy density, i.e. wΛ = −1 . During the matter and radiation-dominated eras the EoS of BD-ΛCDM tracks the dominant component of the univer… view at source ↗

**Figure 1.** In the table, we compare the standard ΛCDM [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

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Reference graph

Works this paper leans on

22 extracted references · 20 canonical work pages · cited by 6 Pith papers

[1]

Abbott, T. M. C., et al. 2019, ApJ, 872, L30. Akaike, H. 1974, IEEE Trans. Autom. Control, 19,

work page 2019
[2]

D, Melchiorri, A., & Mena, O

Valentino, E. D, Melchiorri, A., & Mena, O. 2017, Phys. Rev., D96, 043503. Will, C. 2006, Living Rev. Rel., 9,

work page 2017
[3]

2014, Phys

Avilez, A., & Skordis, C. 2014, Phys. Rev. Lett., 113, 011101. Ballardini, M., Finelli, F., Umilt` a, C., & Paoletti, D. 2016, JCAP, 1605, 067; Rossi, M., et al. arXiv:1906.10218. Blas, D., Lesgourgues, J., & Tram, T. 2011, JCAP, 1107,

arXiv 2014
[8]

2018, Mod

de Cruz P´ erez, J., & Sol` a, J. 2018, Mod. Phys. Lett., A33, 1850228. Gil-Mar´ ın, H.,et al. 2017, MNRAS, 465,

work page 2018
[17]

2011, Living Rev

Uzan, J-P. 2011, Living Rev. Rel., 14,

work page 2011
[22]

B., et al

Zhao, G. B., et al. 2017, Nat. Astron., 1, 627

work page 2017
[34]

2019, Astron

Blomqvist, M., et al. 2019, Astron. Astrophys., 629, A86. Boisseau, B., Esposito-Farese, G., Polarski, D., & Starobinsky, A.A. 2000, Phys. Rev. Lett., 85,

work page 2019
[43]

& de Cruz P´ erez, J

Sol` a, J., G´ omez-Valent, A. & de Cruz P´ erez, J. 2017, Phys. Lett. B, 774,

work page 2017

Show all 22 references

[82]

Peebles, P. J. E. 1993, Principles of Physical Cosmology (Princeton: Princeton Univ. Press). Perlmutter, S., et al. 1999, ApJ, 517,

1993
[85]

M., et al

Scolnic, D. M., et al. 2018, ApJ, 859,

2018
[101]

2018, Int

Sol` a, J. 2018, Int. J. Mod. Phys., D27, 1847029. Sol` a, J., G´ omez-Valent, A. & de Cruz P´ erez, J. 2015, ApJ, 811, L14; 2017, ApJ, 836,

2018
[126]

G., et al

Riess, A. G., et al. 2019, ApJ, 876,

2019
[317]

2019, Phys

Sol` a, J., G´ omez-Valent, A., & de Cruz P´ erez, J. 2019, Phys. Dark. Univ., 25, 100311. Sol` a, J., de Cruz P´ erez, J., & G´ omez-Valent, A. 2018, MNRAS, 478, 4357; 2018, EPL, 121, 39001. Spiegelhalter, D. J., Best, N. G., Carlin, B. P., & Van Der Linde, A., Bayesian measu...

2019
[565]

Planck XIII (2015) results, Ade, P. A. R, et al. 2016, [Planck Collaboration] Cosmological parameters, A&A, 594, A13 Riess, A. G., et al. 1998, AJ, 116,

2015
[583]

2015, JCAP, 1508,

Umilt` a, C., Ballardini, M., Finelli, F., & Paoletti, D. 2015, JCAP, 1508,

2015
[716]

2015, Dark Energy

Amendola L., & Tsujikawa S. 2015, Dark Energy. Theory and Observations (2nd ed.; Cambridge: Cambridge Univ. Press). Brans-Dicke gravity with a cosmological constant 7 Audren, B., Lesgourgues, J., & Benabed, K. 2013, JCAP, 1302,

2015
[1009]

G., et al

Riess, A. G., et al. 2018, ApJ, 853,

2018
[1757]

arXiv:1812.06076

Hildebrandt, H., et al. arXiv:1812.06076. Li, Y-C., Wu, F.-Q., & Chen, X. 2013, Phys. Rev., D 88, 084053. Martinelli, M., Hogg, N.B., Peirone, S., Bruni M. & Wands, D. 2019, MNRAS, 488,

2013 arXiv
[2163]

P., & Anderson

Burnham K. P., & Anderson. D. R. 2002, Model selection and multimodel inference, (New York: Springer). Camacho, H., et al. 2019, MNRAS, 487,

2002
[2236]

Brans, C., & Dicke, R. H. 1961, Phys. Rev., 124, 925; Dicke, R. H. 1962, Phys. Rev., 125,

1961
[3423]

2018, ApJ, 868, 83; 2019, Astrophys

Park, C-G., & Ratra, J. 2018, ApJ, 868, 83; 2019, Astrophys. Space Sci., 364,

2018
[3870]

G., Padilla, A

Clifton, T., Ferreira, P. G., Padilla, A. & Skordis, C. 2012, Phys. Rept., 513,

2012

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

Abbott, T. M. C., et al. 2019, ApJ, 872, L30. Akaike, H. 1974, IEEE Trans. Autom. Control, 19,

work page 2019

[2] [2]

D, Melchiorri, A., & Mena, O

Valentino, E. D, Melchiorri, A., & Mena, O. 2017, Phys. Rev., D96, 043503. Will, C. 2006, Living Rev. Rel., 9,

work page 2017

[3] [3]

2014, Phys

Avilez, A., & Skordis, C. 2014, Phys. Rev. Lett., 113, 011101. Ballardini, M., Finelli, F., Umilt` a, C., & Paoletti, D. 2016, JCAP, 1605, 067; Rossi, M., et al. arXiv:1906.10218. Blas, D., Lesgourgues, J., & Tram, T. 2011, JCAP, 1107,

arXiv 2014

[4] [8]

2018, Mod

de Cruz P´ erez, J., & Sol` a, J. 2018, Mod. Phys. Lett., A33, 1850228. Gil-Mar´ ın, H.,et al. 2017, MNRAS, 465,

work page 2018

[5] [17]

2011, Living Rev

Uzan, J-P. 2011, Living Rev. Rel., 14,

work page 2011

[6] [22]

B., et al

Zhao, G. B., et al. 2017, Nat. Astron., 1, 627

work page 2017

[7] [34]

2019, Astron

Blomqvist, M., et al. 2019, Astron. Astrophys., 629, A86. Boisseau, B., Esposito-Farese, G., Polarski, D., & Starobinsky, A.A. 2000, Phys. Rev. Lett., 85,

work page 2019

[8] [43]

& de Cruz P´ erez, J

Sol` a, J., G´ omez-Valent, A. & de Cruz P´ erez, J. 2017, Phys. Lett. B, 774,

work page 2017