Pith. sign in

REVIEW 2 major objections 4 minor 72 references

Galaxy-cluster gas fractions and Pantheon+ supernovae allow a constant G when supernova luminosity falls with Chandrasekhar mass.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · grok-4.5

2026-07-11 07:11 UTC pith:65J3JBPP

load-bearing objection Careful null-consistent GP reconstruction of G(z) from Mantz f_gas + Pantheon+ under the non-standard n=0.73 channel; transparent that the standard Chandrasekhar scaling is numerically unusable. the 2 major comments →

arxiv 2607.05367 v1 pith:65J3JBPP submitted 2026-07-06 astro-ph.CO gr-qc

Investigating a Possible Variation of the Gravitational Constant Through Gas Mass Fraction Measurements and Type Ia Supernovae Observations

L. R. Cola\c{c}o , R. F. L. Holanda , Marcelo Ferreira This is my paper
classification astro-ph.CO gr-qc
keywords varying gravitational constantgas mass fractionType Ia supernovaeChandrasekhar massGaussian Processesmodified gravityPantheon+
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper asks whether Newton’s gravitational constant G has changed over cosmic time by combining two independent astronomical probes that both feel the local value of G. X-ray measurements of the gas mass fraction inside relaxed galaxy clusters scale directly with G, while the peak brightness of Type Ia supernovae depends on the Chandrasekhar mass of their white-dwarf progenitors, which itself scales as G to the minus three-halves. The authors adopt a non-standard phenomenological relation, motivated by certain scalar-tensor and screened gravity models, in which the standardized supernova luminosity decreases as the Chandrasekhar mass increases. They convert the joint data set into estimates of the dimensionless function φ(z) = G(z)/G0 and reconstruct that function with Gaussian Processes, without assuming any parametric form for its redshift evolution. Within this framework the reconstruction stays consistent with a constant gravitational coupling out to redshift roughly one, although mild low-redshift departures remain allowed by the present uncertainties.

Core claim

When the standardized luminosity of Type Ia supernovae is taken to scale as G to the power 1.46, a Gaussian-Process reconstruction of φ(z) = G(z)/G0 from Mantz et al. cluster gas fractions and Pantheon+ luminosity distances remains compatible with a constant gravitational coupling over 0 ≤ z ≲ 1; only mild, statistically insignificant low-redshift (z < 0.4) departures are permitted.

What carries the argument

The algebraic relation (Eq. 11) that isolates φ(z) by combining the G-dependence of the X-ray gas fraction with the corrected supernova luminosity distance under the non-standard exponent n = 0.73, then reconstructed non-parametrically by a zero-mean Gaussian Process with a squared-exponential kernel.

Load-bearing premise

The analysis discards the standard Chandrasekhar scaling because it produces unstable reconstructions, so the claimed limits on G apply only if the non-standard luminosity-mass relation is the correct one.

What would settle it

A larger, higher-precision sample of relaxed-cluster gas fractions (for example from eROSITA) jointly analyzed under both the standard (n = -3/4) and non-standard (n = 0.73) luminosity-mass relations that either forces φ(z) away from unity at high significance or restores a stable reconstruction under the standard scaling.

Watch this falsifier — get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. The paper reconstructs a possible redshift evolution of the gravitational constant, G(z)=G0 φ(z), with Gaussian Processes by combining Mantz et al. X-ray gas mass fractions of 44 relaxed clusters (0.018≤z≤1.16) with Pantheon+ luminosity distances matched in redshift bins. Both probes are written as functions of G: f_gas ∝ G and, under a non-standard Chandrasekhar–luminosity scaling L_SNe ∝ M_Ch^{-0.97} (hence L_SNe ∝ G^{1.46}), D_L^{SNe}=D_{L,0} φ^{0.73}. The resulting measurement equation (Eq. 11) is sampled via Monte Carlo (including astrophysical priors on γ_g, K and an external Ω_b/Ω_m prior) and reconstructed with a zero-mean GP plus a φ(0)=1 anchor. Within this n=0.73 channel the reconstruction is compatible with constant G over the observed range, with only mild, non-significant low-z (z<0.4) excursions (Fig. 2, Table I). A positivity robustness check via ln φ yields the same qualitative conclusion.

Significance. If the adopted non-standard luminosity–Chandrasekhar scaling is physically realized, the work supplies a clean, largely model-independent null test of G(z) that jointly exploits two independent G-sensitive observables and modern covariance handling (full Pantheon+ matrix for the matched D_L averages, Monte Carlo propagation of large f_gas errors). The non-parametric GP approach, the explicit positivity test, and the transparent listing of astrophysical priors are strengths that make the result falsifiable and reusable. The restriction to n=0.73, however, means the published constraints do not automatically transfer to the conventional L∝ M_Ch channel; the paper is therefore best read as a targeted probe of a specific modified-gravity phenomenology rather than a model-independent bound on G(z).

major comments (2)
  1. End of §II and §IV.A: the analysis is restricted to the non-standard exponent n=0.73 because the standard Chandrasekhar scaling n=-3/4 produces a highly nonlinear map that yields unstable, poorly constrained reconstructions. The abstract, Fig. 2, Table I and the conclusions therefore apply only inside that phenomenological channel. The manuscript should state this limitation more prominently (title/abstract or a dedicated caveat paragraph) and, if feasible, quantify how large the exponent must be before the reconstruction becomes informative, so that readers can judge the domain of validity of the null result.
  2. Eq. (11) and the Monte Carlo pipeline: the reconstructed φ(z) inherits the external priors on γ0, γ1, K0, K1, α and Ω_b/Ω_m. While the paper correctly propagates these uncertainties, it does not show how much of the final error budget (or of the mild low-z wiggle) is driven by the astrophysical priors versus the f_gas and D_L data. A short sensitivity table or a prior-only reconstruction would clarify whether the data or the priors dominate the consistency with φ=1.
minor comments (4)
  1. Fig. 1 caption and §III: the matching criterion |z_GC-z_SN|≤0.005 and the construction of the averaged covariance (Eq. 15) are clear, but a brief statement of how many SNe typically enter each bin would help the reader assess the effective sample size.
  2. Table II lists φ(z) points used for the GP; adding a column for the corresponding f_gas or D_L values (or a machine-readable supplement) would improve reproducibility.
  3. Notation: the same symbol φ is used for the dimensionless G evolution and, in places, for related quantities; a consistent G_eff/G0 or φ_G notation would avoid minor confusion.
  4. References [67,68] on a late-time G transition are cited in the discussion; a one-sentence comparison of the redshift/scale of that transition with the mild low-z feature in Fig. 2 would strengthen the contextualization.

Circularity Check

1 steps flagged

No load-bearing circularity: φ(z) is obtained by direct inversion of independent observables under an openly restricted phenomenological map; the constant-G consistency is not forced by construction or self-citation.

specific steps
  1. other [§IV, paragraph after Eq. (17); Table II]
    "we include an additional data point at z=0 consistent with ϕ(0)=1 (Table II). Nevertheless, in order to avoid introducing potential biases in the reconstruction, we adopt a zero prior mean function"

    Imposing φ(0)=1 as an extra data point is a physical boundary condition (G today equals the laboratory value) rather than a fitted free parameter that is later re-labeled a prediction. It mildly anchors the GP but does not force the reconstructed high-z behavior or the null-result statement; the data points at z>0 remain independent.

full rationale

The central result is a non-parametric GP reconstruction of φ(z) ≡ G(z)/G0 obtained by Monte-Carlo propagation of external data (Mantz et al. f_gas, Pantheon+ luminosity distances, SH0ES M_B, Ω_b/Ω_m prior, and literature γ/K priors) through the inverted measurement equation (11). That equation is the intended model inversion, not a tautology that forces φ ≡ 1. The only mild boundary is the addition of a single data point φ(0) = 1, which is the definition of the present-day G0 and does not determine the high-z reconstruction. The restriction to the non-standard exponent n = 0.73 is an explicit modeling choice (motivated by external semi-analytic light-curve papers) whose numerical necessity is stated openly; it limits the scope of the claim but does not render the reported reconstruction circular. Self-citations appear in the systematics discussion but are not used to justify uniqueness or to close the derivation. The analysis is therefore self-contained against its external benchmarks.

Axiom & Free-Parameter Ledger

7 free parameters · 4 axioms · 0 invented entities

The central null-consistent reconstruction rests on the adopted L–M_Ch phenomenology, the proportionality f_gas∝G under hydrostatic equilibrium, external astrophysical and cosmological priors, and GP hyperparameters. No new particle or force is invented; φ(z) is a dimensionless reparameterization of G(z). Free parameters are mostly nuisance priors and GP length/amplitude scales rather than a parametric G(z) model.

free parameters (7)
  • GP kernel amplitude σ_f and length l
    Maximized via GP log-likelihood (Eq. 17); control smoothness and amplitude of reconstructed φ(z).
  • γ0, γ1 (gas depletion)
    Gaussian/flat priors γ0=0.79±0.07, |γ1|≤0.05; enter Eq. 11 and are sampled in Monte Carlo.
  • K0, K1 (mass calibration)
    Priors K0=0.93±0.11, |K1|≤0.05; scale f_gas and thus φ.
  • α (mass dependence of γ_g)
    Fixed prior α=0.025±0.033 from Mantz et al.; multiplies γ_g.
  • Ω_b/Ω_m
    External galaxy-clustering prior (Krolewski & Percival 2025); multiplies the right-hand side of Eq. 11.
  • M_B (SNe absolute magnitude)
    Fixed to SH0ES value −19.253±0.027 to set absolute D_L scale; directly affects φ amplitude.
  • n (luminosity–Chandrasekhar exponent)
    Fixed to 0.73 from semi-analytic literature; not fitted, but choice selects the entire analysis channel.
axioms (4)
  • domain assumption Under isothermal β-model hydrostatic equilibrium, f_gas ∝ G, so f_gas(z)=φ(z) f_gas,0 when G=G0 φ(z).
    Derived in §II.A from Eqs. 2–5; load-bearing for mapping f_gas to φ.
  • ad hoc to paper Standardized SNe Ia peak luminosity scales as L_SNe ∝ M_Ch^{−0.97}, hence L_SNe ∝ G^{1.46} and D_L^SNe = D_L,0 φ^{0.73}.
    Phenomenological choice motivated by Wright & Li / Sakstein et al.; §II.B. Standard opposite scaling is discarded.
  • domain assumption Gaussian-process prior with zero mean and squared-exponential kernel adequately represents φ(z), with φ(0)=1 enforced by an extra data point.
    §IV; standard GP cosmology practice but shapes allowed low-z features.
  • domain assumption Relaxed-cluster X-ray f_gas at r_2500 and Pantheon+ distances (matched |Δz|≤0.005) are unbiased enough for a joint G test after applying γ and K priors.
    §III and nuisance treatment in §II.A; hydrostatic bias is acknowledged as a residual risk in §IV.

pith-pipeline@v1.1.0-grok45 · 19097 in / 3685 out tokens · 32781 ms · 2026-07-11T07:11:01.920268+00:00 · methodology

0 comments
read the original abstract

In this paper, we investigate a possible time variation of the gravitational constant (G) using a non-parametric approach. Our main cosmological probe is the gas mass fraction of galaxy clusters measured from X-ray observations. We also account for the effect of a varying $G$ on the intrinsic luminosity of type Ia supernovae (SNe Ia) through the Chandrasekhar mass-luminosity relation. We consider a specific phenomenological scenario, motivated by some scalar-tensor and screened modified-gravity frameworks, in which the standardized luminosity of SNe Ia decreases with increasing Chandrasekhar mass. Using gas mass fraction measurements jointly with luminosity distances from the Pantheon+ compilation, we reconstruct the evolution of G through Gaussian Processes. Our results indicate that a constant gravitational coupling remains broadly consistent with the data, although mild low-redshift departures are allowed.

Figures

Figures reproduced from arXiv: 2607.05367 by L. R. Cola\c{c}o, Marcelo Ferreira, R. F. L. Holanda.

Figure 1
Figure 1. Figure 1: FIG. 1: Left Panel: The weighted-average luminosity distances from Pantheon+ dataset [39] for each galaxy cluster. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: reconstruction of [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Left Panel: the reconstruction of the function ln [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Review history (2 revisions) →

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

72 extracted references · 51 linked inside Pith

  1. [1]

    P. A. M. Dirac, Nature139, 323 (1937)

    1937

  2. [2]

    Uzan, Rev

    J.-P. Uzan, Rev. Mod. Phys.75, 403 (2003), arXiv:hep- ph/0205340

    arXiv 2003

  3. [3]

    Uzan, Living Rev

    J.-P. Uzan, Living Rev. Rel.14, 2 (2011), arXiv:1009.5514 [astro-ph.CO]

    Pith/arXiv arXiv 2011

  4. [4]

    C. J. A. P. Martins, (2017), 10.1088/1361-6633/aa860e, arXiv:1709.02923 [astro-ph.CO]

    Pith/arXiv arXiv doi:10.1088/1361-6633/aa860e 2017

  5. [5]

    Uzan, Living Rev

    J.-P. Uzan, Living Rev. Rel.28, 6 (2025), arXiv:2410.07281 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  6. [6]

    J. H. Gundlach and S. M. Merkowitz, Phys. Rev. Lett. 85, 2869 (2000), arXiv:gr-qc/0006043

    Pith/arXiv arXiv 2000

  7. [7]

    Xue, J.-P

    C. Xue, J.-P. Liu, Q. Li, J.-F. Wu, S.-Q. Yang, Q. Liu, C.-G. Shao, L.-C. Tu, Z.-K. Hu, and J. Luo, National Science Review7, 1803 (2020), https://academic.oup.com/nsr/article- pdf/7/12/1803/38880653/nwaa165.pdf

    2020

  8. [8]

    J. H. Gundlach and S. M. Merkowitz, Phys. Rev. Lett. 85, 2869 (2000)

    2000

  9. [9]

    G. M. Tino, Quantum Sci. Technol.6, 024014 (2021), arXiv:2009.01484 [gr-qc]

    Pith/arXiv arXiv 2021

  10. [10]

    Umilt` a, M

    C. Umilt` a, M. Ballardini, F. Finelli, and D. Paoletti, JCAP08, 017 (2015), arXiv:1507.00718 [astro-ph.CO]

    Pith/arXiv arXiv 2015

  11. [11]

    Ballardini, F

    M. Ballardini, F. Finelli, C. Umilt` a, and D. Paoletti, JCAP05, 067 (2016), arXiv:1601.03387 [astro-ph.CO]

    Pith/arXiv arXiv 2016

  12. [12]

    Y. Bai, J. Salvado, and B. A. Stefanek, JCAP10, 029 (2015), arXiv:1505.04789 [hep-ph]

    Pith/arXiv arXiv 2015

  13. [13]

    Xue, Nucl

    S.-S. Xue, Nucl. Phys. B897, 326 (2015), arXiv:1410.6152 [gr-qc]

    Pith/arXiv arXiv 2015

  14. [14]

    Alvey, N

    J. Alvey, N. Sabti, M. Escudero, and M. Fairbairn, Eur. Phys. J. C80, 148 (2020), arXiv:1910.10730 [astro- ph.CO]

    Pith/arXiv arXiv 2020

  15. [15]

    G. B. Gelmini, M. Kawasaki, A. Kusenko, K. Murai, and V. Takhistov, JCAP09, 051 (2020), arXiv:2005.06721 [hep-ph]

    Pith/arXiv arXiv 2020

  16. [16]

    B. R. Zhang, M. J. Childress, T. M. Davis, N. V. Karpenka, C. Lidman, B. P. Schmidt, and M. Smith, Mon. Not. Roy. Astron. Soc.471, 2254 (2017), arXiv:1706.07573 [astro-ph.CO]

    Pith/arXiv arXiv 2017

  17. [17]

    B. S. Wright and B. Li, Phys. Rev. D97, 083505 (2018), arXiv:1710.07018 [astro-ph.CO]

    Pith/arXiv arXiv 2018

  18. [18]

    W. Zhao, B. S. Wright, and B. Li, JCAP10, 052 (2018), arXiv:1804.03066 [astro-ph.CO]

    Pith/arXiv arXiv 2018

  19. [19]

    Vijaykumar, S

    A. Vijaykumar, S. J. Kapadia, and P. Ajith, Phys. Rev. Lett.126, 141104 (2021), arXiv:2003.12832 [gr-qc]

    Pith/arXiv arXiv 2021

  20. [20]

    R. F. L. Holanda, M. Ferreira, and J. E. Gonzalez, Phys. Lett. B868, 139756 (2025), arXiv:2508.00075 [astro- 9 ph.CO]

    Pith/arXiv arXiv 2025

  21. [21]

    Uzan, Reviews of Modern Physics75, 403 (2003), arXiv:hep-ph/0205340 [hep-ph]

    J.-P. Uzan, Reviews of Modern Physics75, 403 (2003), arXiv:hep-ph/0205340 [hep-ph]

    Pith/arXiv arXiv 2003

  22. [22]

    Uzan, Living Reviews in Relativity14, 2 (2011)

    J.-P. Uzan, Living Reviews in Relativity14, 2 (2011)

    2011

  23. [23]

    Amendola, P

    L. Amendola, P. S. Corasaniti, and F. Occhionero, (1999), arXiv:astro-ph/9907222

    Pith/arXiv arXiv 1999

  24. [24]

    Garcia-Berro, E

    E. Garcia-Berro, E. Gaztanaga, J. Isern, O. Benvenuto, and L. Althaus, (1999), arXiv:astro-ph/9907440

    Pith/arXiv arXiv 1999

  25. [25]

    Gaztanaga, E

    E. Gaztanaga, E. Garcia-Berro, J. Isern, E. Bravo, and I. Dominguez, Physical Review D65, 023506 (2001)

    2001

  26. [26]

    Mould and S

    J. Mould and S. Uddin, Publ. Astron. Soc. Austral.31, 15 (2014), arXiv:1402.1534 [astro-ph.CO]

    Pith/arXiv arXiv 2014

  27. [27]

    Rathore, S

    Ruchika, H. Rathore, S. Roy Choudhury, and V. Rentala, JCAP06, 056 (2024), arXiv:2306.05450 [astro-ph.CO]

    arXiv 2024

  28. [28]

    Riazuelo and J.-P

    A. Riazuelo and J.-P. Uzan, Phys. Rev. D66, 023525 (2002)

    2002

  29. [29]

    Loren-Aguilar, E

    P. Loren-Aguilar, E. Garcia-Berro, J. Isern, and Y. A. Kubyshin, Class. Quant. Grav.20, 3885 (2003), arXiv:astro-ph/0309722

    Pith/arXiv arXiv 2003

  30. [30]

    P. Brax, C. van de Bruck, A.-C. Davis, and D. J. Shaw, Phys. Rev. D78, 104021 (2008), arXiv:0806.3415 [astro- ph]

    Pith/arXiv arXiv 2008

  31. [31]

    J. J. Ceron-Hurtado, J.-h. He, and B. Li, Phys. Rev. D 94, 064052 (2016), arXiv:1609.00532 [astro-ph.CO]

    Pith/arXiv arXiv 2016

  32. [32]

    Khoury and A

    J. Khoury and A. Weltman, Phys. Rev. D69, 044026 (2004), arXiv:astro-ph/0309411

    Pith/arXiv arXiv 2004

  33. [33]

    J. Wang, L. Hui, and J. Khoury, Phys. Rev. Lett.109, 241301 (2012), arXiv:1208.4612 [astro-ph.CO]

    Pith/arXiv arXiv 2012

  34. [34]

    Khoury and A

    J. Khoury and A. Weltman, Phys. Rev. Lett.93, 171104 (2004), arXiv:astro-ph/0309300

    Pith/arXiv arXiv 2004

  35. [36]

    Lamine, Y

    B. Lamine, Y. Ozdalkiran, L. Mirouze, F. Erdogan, S. Ilic, I. Tutusaus, R. Kou, and A. Blanchard, Astron. Astrophys.697, A109 (2025), arXiv:2407.15553 [astro- ph.CO]

    Pith/arXiv arXiv 2025

  36. [37]

    Bezerra-Sobrinho, R

    J. Bezerra-Sobrinho, R. R. Cuzinatto, L. G. Medeiros, and P. J. Pompeia, (2025), arXiv:2509.09211 [astro- ph.CO]

    arXiv 2025

  37. [38]

    A. B. Mantz, R. G. Morris, S. W. Allen, R. E. A. Canning, L. Baumont, B. Benson, L. E. Bleem, S. R. Ehlert, B. Floyd, R. Herbonnet, P. L. Kelly, S. Liang, A. von der Linden, M. McDonald, D. A. Rapetti, R. W. Schmidt, N. Werner, and A. Wright, Monthly Notices of the Royal Astronomical Society510, 131 (2021), https://academic.oup.com/mnras/article- pdf/510/...

    2021

  38. [39]

    Scolnicet al., Astrophys

    D. Scolnicet al., Astrophys. J.938, 113 (2022), arXiv:2112.03863 [astro-ph.CO]

    Pith/arXiv arXiv 2022

  39. [40]

    S. W. Allen, A. E. Evrard, and A. B. Mantz, ARAA49, 409 (2011), arXiv:1103.4829 [astro-ph.CO]

    Pith/arXiv arXiv 2011

  40. [41]

    R. F. L. Holanda, S. H. Pereira, and S. Santos da Costa, prd95, 084006 (2017), arXiv:1612.09365 [astro-ph.CO]

    Pith/arXiv arXiv 2017

  41. [42]

    Sasaki, PASJ48, L119 (1996), arXiv:astro-ph/9611033 [astro-ph]

    S. Sasaki, PASJ48, L119 (1996), arXiv:astro-ph/9611033 [astro-ph]

    Pith/arXiv arXiv 1996

  42. [43]

    C. L. Sarazin,X-ray emission from clusters of galaxies (1988)

    1988

  43. [44]

    Allen, D

    S. Allen, D. Rapetti, R. Schmidt, H. Ebeling, R. Morris, and A. Fabian, Monthly Notices of the Royal Astronom- ical Society383, 879 (2008)

    2008

  44. [45]

    Ettori, A

    S. Ettori, A. Morandi, P. Tozzi, I. Balestra, S. Borgani, P. Rosati, L. Lovisari, and F. Terenziani, aap501, 61 (2009), arXiv:0904.2740 [astro-ph.CO]

    Pith/arXiv arXiv 2009

  45. [47]

    Holanda, R

    R. Holanda, R. Gon¸ calves, J. Gonzalez, and J. Alcaniz, Journal of Cosmology and Astroparticle Physics2019, 032–032 (2019)

    2019

  46. [48]

    D. E. Applegate, A. von der Linden, P. L. Kelly, M. T. Allen, S. W. Allen, P. R. Burchat, D. L. Burke, H. Ebel- ing, A. Mantz, and R. G. Morris, Monthly Notices of the Royal Astronomical Society439, 48 (2014)

    2014

  47. [49]

    A. B. Mantz, S. W. Allen, R. G. Morris, D. A. Rapetti, D. E. Applegate, P. L. Kelly, A. von der Linden, and R. W. Schmidt, Mon. Not. Roy. Astron. Soc.440, 2077 (2014), arXiv:1402.6212 [astro-ph.CO]

    Pith/arXiv arXiv 2077

  48. [50]

    Battaglia, J

    N. Battaglia, J. Bond, C. Pfrommer, and J. Sievers, apj 777, 123 (2013), arXiv:1209.4082 [astro-ph.CO]

    Pith/arXiv arXiv 2013

  49. [51]

    Battaglia, J

    N. Battaglia, J. Bond, C. Pfrommer, and J. Sievers, The Astrophysical Journal777, 123 (2013)

    2013

  50. [52]

    Planelles, S

    S. Planelles, S. Borgani, K. Dolag, S. Ettori, D. Fabjan, G. Murante, and L. Tornatore, Monthly Notices of the Royal Astronomical Society431, 1487 (2013)

    2013

  51. [53]

    R. F. L. Holanda, V. C. Busti, J. E. Gonzalez, F. Andrade-Santos, and J. S. Alcaniz, (2017), arXiv:1706.07321 [astro-ph.CO]

    Pith/arXiv arXiv 2017

  52. [54]

    Krolewski and W

    A. Krolewski and W. J. Percival, Phys. Rev. D111, 063526 (2025), arXiv:2403.19236 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  53. [55]

    S. E. Woosley and T. A. Weaver, IN: Annual review of astronomy and astrophysics. Volume 24 (A87-26730 10- 90). Palo Alto, CA, Annual Reviews, Inc., 1986, p. 205- 253.24, 205 (1986)

    1986

  54. [56]

    Brans and R

    C. Brans and R. H. Dicke, Phys. Rev.124, 925 (1961)

    1961

  55. [57]

    Li, F.-Q

    J.-X. Li, F.-Q. Wu, Y.-C. Li, Y. Gong, and X.- L. Chen, Res. Astron. Astrophys.15, 2151 (2015), arXiv:1511.05280 [astro-ph.CO]

    Pith/arXiv arXiv 2015

  56. [58]

    V. H. Hamity and D. E. Barraco, Class. Quant. Grav. 22, 3841 (2005), arXiv:gr-qc/0504105

    Pith/arXiv arXiv 2005

  57. [59]

    R. P. Gupta, Mon. Not. Roy. Astron. Soc.511, 4238 (2022), arXiv:2112.10654 [gr-qc]

    Pith/arXiv arXiv 2022

  58. [60]

    Ballardini and F

    M. Ballardini and F. Finelli, Phys. Rev. D106, 063531 (2022), arXiv:2112.15126 [astro-ph.CO]

    Pith/arXiv arXiv 2022

  59. [61]

    Sakstein, H

    J. Sakstein, H. Desmond, and B. Jain, Phys. Rev. D 100, 104035 (2019), arXiv:1907.03775 [astro-ph.CO]

    Pith/arXiv arXiv 2019

  60. [62]

    A. G. Riess, W. Yuan, L. M. Macri, D. Scolnic, D. Brout, S. Casertano, D. O. Jones, Y. Murakami, G. S. Anand, L. Breuval,et al., The Astrophysical journal letters934, L7 (2022)

    2022

  61. [63]

    Ferreira, R

    M. Ferreira, R. F. L. Holanda, J. E. Gonzalez, L. R. Cola¸ co, and R. C. Nunes, Eur. Phys. J. C84, 1120 (2024), arXiv:2410.21542 [astro-ph.CO]

    Pith/arXiv arXiv 2024

  62. [64]

    Cola¸ co, R

    L. Cola¸ co, R. Holanda, and R. C. Nunes, arXiv preprint arXiv:2201.04073 (2022)

    Pith/arXiv arXiv 2022

  63. [66]

    Seikel, C

    M. Seikel, C. Clarkson, and M. Smith, JCAP1206, 036 (2012), arXiv:1204.2832 [astro-ph.CO]

    Pith/arXiv arXiv 2012

  64. [67]

    Perivolaropoulos, and A

    Ruchika, L. Perivolaropoulos, and A. Melchiorri, Phys. Rev. D111, 123526 (2025), arXiv:2408.03875 [astro- ph.CO]

    arXiv 2025

  65. [68]

    Perivolaropoulos and Ruchika, Phys

    L. Perivolaropoulos and Ruchika, Phys. Rev. D113, 023501 (2026)

    2026

  66. [69]

    J. E. Gonzalez, M. Ferreira, L. R. Cola¸ co, R. F. L. Holanda, and R. C. Nunes, Phys. Lett. B857, 138982 (2024), arXiv:2405.13665 [astro-ph.CO] . 10

    Pith/arXiv arXiv 2024

  67. [70]

    L. R. Cola¸ co, R. F. L. Holanda, Z. C. Santana, and R. Silva, Eur. Phys. J. C85, 577 (2025), arXiv:2505.17262 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  68. [71]

    L. R. Cola¸ co, Universe11, 89 (2025), arXiv:2503.06189 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  69. [72]

    L. R. Cola¸ co, M. Ferreira, R. F. L. Holanda, J. E. Gonzalez, and R. C. Nunes, JCAP05, 098 (2024), arXiv:2310.18711 [astro-ph.CO]

    Pith/arXiv arXiv 2024

  70. [73]

    L. R. Cola¸ co, S. J. Landau, J. E. Gonzalez, J. Spinelly, and G. L. F. Santos, JCAP08, 062 (2022), arXiv:2204.06459 [astro-ph.CO]

    Pith/arXiv arXiv 2022

  71. [74]

    L. R. Cola¸ co, J. E. Gonzalez, and R. F. L. Holanda, Eur. Phys. J. C81, 533 (2021), arXiv:2010.04021 [astro- ph.CO]

    Pith/arXiv arXiv 2021

  72. [75]

    L. R. Cola¸ co, R. F. L. Holanda, and R. Silva, Eur. Phys. J. C81, 822 (2021), arXiv:2004.08484 [astro-ph.CO]

    Pith/arXiv arXiv 2021