Pith. sign in

REVIEW 4 major objections 5 minor 51 references

Rainbow Gauss-Bonnet gravity can reproduce the observed baryon-to-entropy ratio by keeping the time derivative of the Ricci scalar nonzero during radiation domination.

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 · deepseek-v4-flash

2026-08-01 02:17 UTC pith:2BRGBTYF

load-bearing objection Combining 4D EGB with rainbow gravity for baryogenesis is a legitimate idea and the analytic machinery is mostly real, but the numerical claims are unsupported because the effective operator is used far above its cutoff; the stress-test arithmetic is wrong, though the paper still has real problems. the 4 major comments →

arxiv 2607.25491 v1 pith:2BRGBTYF submitted 2026-07-28 gr-qc

Gravitational Baryogenesis in Rainbow Gauss-Bonnet gravity

P. Goodarzi , H. Mohseni Sadjadi , R. Darabi This is my paper
classification gr-qc
keywords gravitational baryogenesisEinstein-Gauss-Bonnet gravityrainbow gravitybaryon-to-entropy ratioradiation dominationmodified Friedmann equationeffective field theory
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.

The paper claims that combining regularized four-dimensional Einstein-Gauss-Bonnet gravity with rainbow-gravity metric corrections removes the main obstacle to gravitational baryogenesis: during radiation domination the Ricci scalar is constant in general relativity, so its time derivative vanishes and no asymmetry is generated. In this combined framework, the Gauss-Bonnet sector introduces a quartic Hubble term that makes the Ricci scalar's time derivative nonzero even for a radiation equation of state. The authors derive analytic expressions for the baryon-to-entropy ratio in the high-curvature and perturbative regimes, and they identify parameter spaces that numerically reproduce the observed Y_B ~ 10^-10. The mechanism is purely gravitational in origin, needing no new matter fields beyond the standard baryon-number-violating interactions.

Core claim

In the regularized four-dimensional Einstein-Gauss-Bonnet action with a rainbow metric, the modified Friedmann equation becomes alpha H^4 + H^2 = rho/(3 M_P^2). Because the Ricci scalar is R = 6 H' + 12 H^2, the alpha H^4 term prevents R from being constant during radiation domination. Using the standard gravitational-baryogenesis interaction S_int = (1/M_*^2) ∫ d^4x sqrt(-g) (∂_mu R) J^mu, the paper computes the induced chemical potential mu_B = R-dot/M_*^2 and hence the baryon-to-entropy ratio at the decoupling temperature. It finds a nonzero asymmetry at w = 1/3 in the high-curvature regime, and in the perturbative regime the leading term vanishes at w = 1/3 while the order-alpha Gauss-Bo

What carries the argument

The central machinery is the regularized four-dimensional Einstein-Gauss-Bonnet action — a scalar-tensor theory obtained from the D→4 limit of the Gauss-Bonnet term that keeps the field equations second-order — combined with rainbow gravity's energy-dependent metric. The load-bearing equation is the modified Friedmann equation alpha H^4 + H^2 = rho/(3 M_P^2), whose quartic Hubble term changes the background evolution enough to make R-dot nonzero during radiation domination. The asymmetry engine is the effective operator S_int = (1/M_*^2) ∫ d^4x sqrt(-g) (∂_mu R) J^mu, which acts as a chemical potential mu_B = R-dot/M_*^2; the final asymmetry is evaluated when the baryon-number-violating rate

Load-bearing premise

The effective interaction between ∂_mu R and the baryon current is treated as valid at decoupling temperatures hundreds of times above its cutoff M_*, and the paper never enforces the condition T_D ≲ M_*.

What would settle it

Rerun the numerical analysis with the effective-field-theory validity condition T_D ≤ M_* imposed; if no parameter set in either regime still yields Y_B ≈ 6 x 10^-10, the central claim is falsified. The decisive numbers are already in Tables 5.1 and 5.2, where every quoted viable row has T_D/M_* of at least roughly 300.

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

If this is right

  • Gravitational baryogenesis from the Ricci scalar works during the radiation era in this model, closing a gap in the standard mechanism.
  • The produced asymmetry is sensitive to the Gauss-Bonnet coupling alpha, the rainbow scale M, and the rainbow parameter beta, so a precision measurement of Y_B could constrain modified-gravity parameters.
  • Larger values of the rainbow parameter beta systematically suppress Y_B, meaning quantum-gravity corrections tend to reduce the efficiency of baryogenesis.
  • The decoupling temperature T_D is shifted by the combined Gauss-Bonnet and rainbow corrections relative to standard cosmology, altering the relation between the baryon-violating scale M_B and freeze-out.
  • Both the perturbative and high-curvature regimes contain parameter sets reaching Y_B ~ 10^-10, so the mechanism is not confined to a single limiting case.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The paper never imposes the effective-field-theory consistency bound T_D ≲ M_*; its own tables use T_D/M_* of order 300 or more, so redoing the numerical scan with that bound enforced may erase the quoted viable regions.
  • If the mechanism survives that consistency check, the baryon asymmetry of the Universe becomes a probe of Planck-scale curvature corrections at temperatures near 10^13 GeV.
  • The same design principle — any higher-curvature term that keeps R-dot nonzero during radiation domination — should rescue gravitational baryogenesis in other modified-gravity theories, suggesting a general feature rather than a unique property of Einstein-Gauss-Bonnet gravity.
  • The required Gauss-Bonnet couplings, alpha between 10^16 and 10^23 M_P^-2, lie far above typical observational bounds on such couplings; checking compatibility with those bounds is a direct next step.

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

4 major / 5 minor

Summary. The paper studies gravitational baryogenesis in a regularized four-dimensional Einstein-Gauss-Bonnet (EGB) gravity with rainbow-gravity corrections. It derives analytic expressions for the baryon-to-entropy ratio Y_B in two regimes, αH^2 ≫ 1 and αH^2 ≪ 1, and argues that the Gauss-Bonnet term yields a nonvanishing Ṙ during radiation domination, where the Einstein-Hilbert contribution vanishes. Numerical tables and contour plots are presented to identify parameter regions that supposedly satisfy theoretical constraints and reproduce the observed Y_B ~ 10^-10. The central claim is that the combined Rainbow-EGB framework resolves the radiation-era problem of standard gravitational baryogenesis.

Significance. If the numerical and analytic results were correct, the paper would offer a phenomenologically interesting mechanism for generating the baryon asymmetry during the radiation era. The paper also has some strengths: it attempts a systematic treatment of both regimes, and it provides explicit formulas and tables. However, the central numerical claim is not established because of internal inconsistencies and because the effective-theory validity is violated by the parameter choices. The seven-parameter scan is a fit to the observed value rather than an independent prediction, which further weakens the claim that the model 'reproduces' Y_B.

major comments (4)
  1. [§4, Eqs. (50)–(52)] Eq. (52) is identical to Eq. (50), although the text says it is the result of substituting Eq. (51) into Ṙ and retaining terms to O(α). The substitution is therefore not actually performed as printed. Eq. (53) appears to contain a corrected α-dependent bracket, but the intermediate step is wrong and makes the perturbative derivation internally inconsistent.
  2. [§5, Tables 5.1 and 5.2] The numerical analysis evaluates Eq. (25) at decoupling temperatures T_D ~ 10^13–10^14 GeV while using M_* = 10^-8 M_P (Table 5.1) and M_* = 10^-9 M_P (Table 5.2). Thus T_D/M_* ~ 10^3–10^4. The effective interaction (20) with cutoff M_* is not valid in this regime. The paper never states or enforces T_D < M_*, so the tabulated Y_B values are not justified by a controlled effective field theory.
  3. [§5.1, Table 5.1] Table 5.1 is not consistent with the paper's own formulas. Rows 2 and 6 have the same (α,β,n,M_B,M_*) and differ only by M (9×10^-12 vs 9×10^-11 M_P). Equation (57) gives T_D ∝ M^{1/8}, matching the tabulated T_D increase from 3.49×10^13 to 4.65×10^13 GeV. But Eq. (53) for the α term scales as M^{1/2} T_D^8, so Y_B should increase by a factor ~31, not decrease from 5.2×10^-11 to 1.6×10^-11. The table therefore cannot have been generated from Eqs. (53) and (57).
  4. [§5.2, Eq. (62)] Equation (62) is dimensionally inconsistent. The combination inside the parentheses, √ρ/(√3 α M^2 M_P), has mass dimension 1 (√ρ ~ mass^2, α ~ mass^-2, M^2M_P ~ mass^3). Since X is defined in Eq. (58) as a dimensionless ratio, Eq. (62) cannot be used to impose the constraint X ≫ 1. This affects the contour plots in Fig. 5 and the high-curvature numerical scan.
minor comments (5)
  1. [§5, first paragraph] The text says '˜f≈(H/M)^α' during the early universe; this should presumably be '(H/M)^β'.
  2. [§3, Eq. (34)] The sentence introducing Eq. (34) is garbled: 'the physical Hubble parameter is related to H by H=H/f(T)'. Please clarify which H (rainbow-time or physical) appears in each equation.
  3. [Tables 5.1 and 5.2] The tables do not list the values of g_b and g_* used, nor the convention for M_P (reduced or Planck). This makes the numerical entries hard to reproduce.
  4. [References] References [47] and [49] duplicate [35] and [41], respectively.
  5. [§5.1, Table 5.1] A check of Eq. (57) for row 3 gives T_D ≈ 3.5×10^13 GeV, so the tabulated T_D values are not off by orders of magnitude. The inconsistency I find is in the Y_B scaling, not the freeze-out temperature.

Circularity Check

1 steps flagged

Numerical Y_B match is a free-parameter fit, while the analytical nonzero-˙R derivation is independent.

specific steps
  1. fitted input called prediction [Section 5, opening paragraph (before Eq. (58)); used in Tables 5.1/5.2 and Conclusion]
    "We have identified seven parameters in the model, denoted as w, α, β, n, M, MB, M⋆. These parameters are determined by requiring the resulting baryon-to-entropy ratio to be consistent with current cosmological observations while simultaneously satisfying the theoretical constraints of the model."

    The numerical 'reproduction' of Y_B ~ 10^-10 is not an independent model output: the free parameters, especially M_*, which enters Y_B only through 1/M_*^2 in Eqs. (37), (43), and (53), are explicitly selected to make the computed ratio equal the observed target. The conclusion's claim of 'viable parameter spaces reproducing the observed Y_B' therefore reduces by construction to the fitted input. The analytical nonzero-˙R result is independent, so the circularity is partial.

full rationale

The analytical derivation is self-contained: the modified Friedmann equations (14)-(19) follow from the action; the Ricci scalar and its derivative are computed from the metric and field equations (27)-(36), (50)-(53); and the baryon-to-entropy ratio (25) is evaluated at a freeze-out temperature fixed by (40)-(42)/(57). The key qualitative result, that ˙R and hence Y_B do not vanish at w=1/3, is an algebraic consequence of the EGB correction and does not use the observed Y_B. The numerical section, however, explicitly states that its seven parameters are determined by requiring consistency with observations, so the tabulated agreement with Y_B ~ 10^-10 is a fit rather than a prediction; this is a partial circularity in the validation claim but not in the formal derivation. The power-law rainbow function is adopted from external references, not from the authors' own prior work, and the self-citations in the introduction (e.g., refs. [19,20,26,29]) are background rather than load-bearing. The EFT-validity issue (T_D >> M_* in some rows) is a correctness concern, not a circularity.

Axiom & Free-Parameter Ledger

7 free parameters · 5 axioms · 0 invented entities

The central claim rests on seven scanned free parameters and several domain assumptions (Horndeski validity of 4D EGB, ad hoc rainbow function, EFT validity of the baryogenesis operator, freeze-out rate). No new particles are introduced.

free parameters (7)
  • α (GB coupling) = 10^15 – 10^25 M_P^{-2} (Tables 5.1, 5.2)
    Scanned to make Y_B match observations; no independent constraint applied.
  • β (rainbow parameter) = 1.0 – 1.2
    Scanned; controls suppression of Y_B.
  • M (rainbow energy scale) = 9×10^-12 M_P, 10^-12 M_P, 10^-11 M_P
    Scanned; enters through f(T) ≈ (H/M)^β.
  • M_B (B-violating scale) = 10^-4 to 10^-3 M_P
    Scanned; sets freeze-out via Γ_B = T^{2n+1}/M_B^{2n}.
  • M_* (cutoff of ∂R J interaction) = 10^-8 M_P or 10^-9 M_P
    Scanned; chosen low to boost Y_B, but creates T_D ≫ M_* inconsistency.
  • n (mass dimension of B-violating operator minus 4) = n=2 in tables (also 1,3 in figures)
    Chosen; affects Γ_B and T_D scaling.
  • w (equation of state) = 1/3 for radiation era (also varied in figures)
    Set to target radiation dominance; not constrained externally.
axioms (5)
  • domain assumption The regularized 4D EGB action (5) is a valid Horndeski scalar-tensor theory obtained from the D→4 limit of (2).
    Invoked at Eq. (5); the Glavan-Lin construction is cited but its consistency has been debated; if invalid, the Friedmann equations (14)-(19) do not apply.
  • ad hoc to paper The rainbow function has the power-law form f² = 1+(H/M)^{2β} and f ≈ (H/M)^β during the early universe.
    Eqs. (11)-(12); chosen by hand from refs [51,52]; no derivation from quantum gravity; load-bearing for all β-scaling.
  • ad hoc to paper The effective operator (20) with cutoff M_* gives the chemical potential μ_B = R-dot / M_*² and is valid at the decoupling temperature.
    Eqs. (20)-(25); the paper uses T_D ≫ M_*, so the EFT is used outside its validity.
  • domain assumption B-violating interactions freeze out when Γ_B(T_D) = H(T_D), with Γ_B = T^{2n+1}/M_B^{2n}.
    Eqs. (39)-(40); standard baryogenesis assumption, but not tied to a concrete particle model.
  • ad hoc to paper The scalar field solution φ' = H + C/A with C=0 (dark radiation ignored).
    Eq. (16) and §2: 'We ignore the dark radiation, C=0'; this removes a term that could affect the background evolution.

pith-pipeline@v1.3.0-alltime-deepseek · 14241 in / 33238 out tokens · 288624 ms · 2026-08-01T02:17:32.836726+00:00 · methodology

0 comments
read the original abstract

The gravitational baryogenesis is studied in regularized four dimensional Einstein Gauss Bonnet model with rainbow gravity corrections. This combined framework generates a non vanishing time derivative of the Ricci scalar even during radiation domination era. We derive analytical expressions for the baryon to entropy ratio in both the high curvature and perturbative regimes. The Gauss Bonnet contribution produces nonzero asymmetry precisely at radiation era, where the Einstein Hilbert contribution vanishes. Numerical analysis identifies viable parameter spaces reproducing the observed baryon to entropy ratio, compatible with observations.

Figures

Figures reproduced from arXiv: 2607.25491 by H. Mohseni Sadjadi, P. Goodarzi, R. Darabi.

Figure 1
Figure 1. Figure 1: Contour plots are presented to identify plausible values for the parameters α, β, M and MB, under the constraints Z ≪ 1 and X ≫ 1. The top three plots show results for w = 1/3, n = 2, M = 9 × 10−12Mp, MB = 3 × 10−4Mp, and M⋆ = 10−8Mp. The bottom three plots illustrate results for, α = 1016M−2 p , β = 1, w = 1/3, n = 2, and M⋆ = 10−8Mp. 5 Numerical analyses In the preceding section, we analytically investig… view at source ↗
Figure 2
Figure 2. Figure 2: We present a comparison of the baryon-to-entropy ratio for the Einstein-Hilbert action (Y EH B , solid lines) and the Gauss-Bonnet action (Y GB B , dashed lines) as a function of the equation of state w. These results are shown for several values of the rainbow parameter β ∈ {1.00, 1.05, 1.10} within the regime Z ≪ 1. In these plots we assume that, α = 1016M−2 p , β = 1, n = 2, M = 9 × 10−12Mp, MB = 3 × 10… view at source ↗
Figure 3
Figure 3. Figure 3: We present the baryon-to-entropy ratio as a function of α, n, M, MB, and w, for several different values of the rainbow parameter β ∈ {1.00, 1.05, 1.10} within the regime Z ≪ 1. For any parameters not varied in the plots, we have adopted the following values: α = 1016M−2 p , β = 1, n = 2, M = 9 × 10−12Mp, MB = 3 × 10−4Mp and M⋆ = 10−8Mp. X ≈  ρ 3M2M2 p  1 β+1 , (60) Z ≈ αρ 3M2 p . (61) In this regime, th… view at source ↗
Figure 4
Figure 4. Figure 4: We present the baryon-to-entropy ratio as a function of β, n, M, MB, and w, for several different values of the Gauss-Bonnet coupling constant α ∈ {1016M−2 p , 2 × 1016M−2 p , 4 × 1016M−2 p } within the regime Z ≪ 1. For any parameters not varied in the plots, we have adopted the following values: β = 1, β = 1, n = 2, M = 9 × 10−12Mp, MB = 3 × 10−4Mp and M⋆ = 10−8Mp. of YB (right panel) demonstrates a char… view at source ↗
Figure 5
Figure 5. Figure 5: Contour plots are presented to identify plausible values for the parameters α, β, M and MB, under the constraints Z ≫ 1 and X ≫ 1. The top three plots show results for w = 1/3, n = 2, M = 10−12Mp, MB = 10−4Mp, and M⋆ = 10−9Mp. The bottom three plots illustrate results for, α = 1023M−2 p , β = 1, w = 1/3, n = 2, and M⋆ = 10−9Mp. remains negligible throughout the majority of the specified w domain, con￾siste… view at source ↗
Figure 6
Figure 6. Figure 6: We present the baryon-to-entropy ratio as a function of α, n, M, MB, and w, for several different values of the rainbow parameter β ∈ {1.0, 1.1, 1.2} within the regime Z ≫ 1. For any parameters not varied in the plots, we have adopted the following values: w = 1/3, α = 1023M−2 p , β = 1, n = 2, M = 10−12Mp, MB = 10−3Mp and M⋆ = 10−9Mp. respect to the parameters β, n, M, w and MB we present [PITH_FULL_IMAG… view at source ↗
Figure 7
Figure 7. Figure 7: We present the baryon-to-entropy ratio as a function of β, n, M, MB, and w, for several different values of the Gauss-Bonnet coupling constant α ∈ {1023M−2 p , 5 × 1023M−2 p , 1024M−2 p } within the regime Z ≫ 1. For any parameters not varied in the plots, we have adopted the following values: w = 1/3, β = 1, n = 2, M = 10−12Mp, MB = 10−3Mp and M⋆ = 10−9Mp. ratio YB within the Z ≪ 1 regime for radiation-do… view at source ↗

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

51 extracted references · 33 linked inside Pith

  1. [1]

    Aghanim et al

    N. Aghanim et al. [Planck Collaboration], Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020), arXiv:1807.06209 [astro-ph.CO]

    Pith/arXiv arXiv 2018

  2. [2]

    R. L. Workman et al. [Particle Data Group], Review of Particle Physics, Prog. Theor. Exp. Phys. 2022, 083C01 (2022)

    2022

  3. [3]

    A. D. Sakharov, JETP Lett. 5, 24 (1967)

    1967

  4. [4]

    E. W. Kolb and M. S. Turner,The Early Universe, Addison-Wesley, Reading, MA (1990)

    1990

  5. [5]

    Riotto and M

    A. Riotto and M. Trodden, Ann. Rev. Nucl. Part. Sci. 49, 35 (1999), arXiv:hep-ph/9901362

    Pith/arXiv arXiv 1999

  6. [6]

    Affleck and M

    I. Affleck and M. Dine, Nucl. Phys. B 249, 361 (1985)

    1985

  7. [7]

    V. A. Kuzmin, V. A. Rubakov, and M. E. Shaposhnikov, Phys. Lett. B 155, 36 (1985)

    1985

  8. [8]

    Fukugita and T

    M. Fukugita and T. Yanagida, Phys. Lett. B 174, 45 (1986)

    1986

  9. [9]

    A. G. Cohen and D. B. Kaplan, Nucl. Phys. B 308, 913 (1988)

    1988

  10. [10]

    Arbuzova, A.D

    E.V. Arbuzova, A.D. Dolgov, V.A. Novikov, Phys. Rev. D 94, 123501 (2016), arXiv:1607.01247 [astro-ph.CO]

    Pith/arXiv arXiv 2016

  11. [11]

    Dubbini, O

    M. Dubbini, O. Luongo, A. Quaranta, Phys. Rev. D 113, 043523 (2026), arXiv:2505.03644 [gr-qc]

    Pith/arXiv arXiv 2026

  12. [12]

    Davoudiasl, R

    H. Davoudiasl, R. Kitano, G. D. Kribs, H. Murayama, and P. J. Stein- hardt, Phys. Rev. Lett. 93, 201301 (2004), arXiv:hep-ph/0403019

    Pith/arXiv arXiv 2004

  13. [13]

    Arbuzova and A

    E. Arbuzova and A. Dolgov JCAP 06(2017)001, arXiv:1702.07477 [gr- qc]

    Pith/arXiv arXiv 2017

  14. [14]

    Zhong-Wen Feng et al JCAP06(2022)022, arXiv:2203.11671 [gr-qc]

    Pith/arXiv arXiv 2022

  15. [15]

    M. A. Mojahed, K. Schmitz, Xun-Jie Xu, Phys. Rev. D 111, 055005 (2025), arXiv:2409.10605 [hep-ph]. 22

    Pith/arXiv arXiv 2025

  16. [16]

    Saaidi, and H

    Kh. Saaidi, and H. Hossienkhani, Astrophys. Space Sci. 333, 305 (2011), arXiv:1010.4966 [gr-qc]

    Pith/arXiv arXiv 2011

  17. [17]

    De Felice and S

    A. De Felice and S. Tsujikawa, Living Rev. Relativ. 13, 3 (2010), arXiv:1002.4928 [gr-qc]

    Pith/arXiv arXiv 2010

  18. [18]

    Lambiase and S

    G. Lambiase and S. Mohanty, Phys. Rev. D 74, 123509 (2006), arXiv:hep-ph/0504113

    Pith/arXiv arXiv 2006

  19. [19]

    Mohseni Sadjadi, Phys

    H. Mohseni Sadjadi, Phys. Rev. D 77, 103501 (2008), arXiv:0710.3308 [gr-qc]

    Pith/arXiv arXiv 2008

  20. [20]

    Goodarzi, JHEP 02, 029 (2026), arXiv:2508.16955 [gr-qc]

    P. Goodarzi, JHEP 02, 029 (2026), arXiv:2508.16955 [gr-qc]

    arXiv 2026

  21. [21]

    Oikonomou, E

    V.K. Oikonomou, E. N. Saridakis, Phys. Rev. D 94, 124005 (2016), arXiv:1607.08561 [gr-qc]

    Pith/arXiv arXiv 2016

  22. [22]

    Malakar, R

    K. Malakar, R. Mazumdar, M. M. Gohain, K. Bhuyan, arXiv:2509.03053 [gr-qc]

    arXiv

  23. [23]

    D. F.P. Cruz, D. S. Pereira, F. S.N. Lobo, Nucl. Phys. B 1023 (2026) 117304, arXiv:2509.17218 [gr-qc]

    arXiv 2026

  24. [24]

    Bhattacharjee, Phys

    S. Bhattacharjee, Phys. Dark Univ. 30, 100612 (2020), arXiv:2005.05534 [gr-qc]

    Pith/arXiv arXiv 2020

  25. [25]

    D. S. Pereira, Phys. Lett. B 875, 140312 (2026), arXiv:2412.06984 [gr- qc]

    arXiv 2026

  26. [26]

    Mohseni Sadjadi, Phys

    H. Mohseni Sadjadi, Phys. Rev. D 76, 123507 (2007), arXiv:0709.0697 [gr-qc]

    Pith/arXiv arXiv 2007

  27. [27]

    S. D. Odintsov and V. K. Oikonomou, Phys. Lett. B 760, 259 (2016), arXiv:1607.00545 [gr-qc]

    Pith/arXiv arXiv 2016

  28. [28]

    B. Feng, H. Li, M. Li and X. Zhang, Phys. Lett. B 620, 27 (2005), arXiv:hep-ph/0406269

    Pith/arXiv arXiv 2005

  29. [29]

    Goodarzi, Eur

    P. Goodarzi, Eur. Phys. J. C 83, 990 (2023), arXiv:2307.10709 [hep-th]

    Pith/arXiv arXiv 2023

  30. [30]

    Zimdahl, Phys

    W. Zimdahl, Phys. Rev. D 53, 5483 (1996), arXiv:astro-ph/9601189

    Pith/arXiv arXiv 1996

  31. [31]

    T.Harko and F.S.N.Lobo, Eur. Phys. J. C 70, 373 (2010), arXiv:1008.4193 [gr-qc]

    Pith/arXiv arXiv 2010

  32. [32]

    Lambiase and S.Mohanty, JCAP 0712, 008 (2007), arXiv:astro- ph/0611905

    G. Lambiase and S.Mohanty, JCAP 0712, 008 (2007), arXiv:astro- ph/0611905

    arXiv 2007

  33. [33]

    Fujii, K

    M. Fujii, K. Hamaguchi and T.Yanagida, Phys. Rev. D 65, 115012 (2002), arXiv:hep-ph/0202210. 23

    Pith/arXiv arXiv 2002

  34. [34]

    Lovelock, J

    D. Lovelock, J. Math. Phys. 12, 498 (1971)

    1971

  35. [36]

    D. G. Boulware and S. Deser, Phys. Rev. Lett. 55, 2656 (1985)

    1985

  36. [37]

    Glavan and C

    D. Glavan and C. Lin, Phys. Rev. Lett. 124, 081301 (2020), arXiv:1905.03601

    Pith/arXiv arXiv 2020

  37. [38]

    R. A. Hennigar, D. Kubiznak, R. B. Mann, C. Pollack, J. High Energ. Phys. 2020, 27 (2020), arXiv:2004.09472 [gr-qc]

    Pith/arXiv arXiv 2020

  38. [39]

    C. M. A. Zanoletti, B. R. Hull, C. D. Leonard, R. B. Mann, JCAP 01, 043(2024), arXiv:2310.19871 [astro-ph.CO]

    Pith/arXiv arXiv 2024

  39. [40]

    G¨ urses, T

    M. G¨ urses, T. C ¸ . S ¸i¸ sman and B. Tekin, Eur. Phys. J. C 80, 647 (2020), arXiv:2004.03390 [gr-qc]

    Pith/arXiv arXiv 2020

  40. [42]

    T.Kobayashi, JCAP 07, 013 (2020), arXiv:2003.12771 [gr-qc]

    Pith/arXiv arXiv 2020

  41. [43]

    K. Aoki, M. A. Gorji and S. Mukohyama, Phys. Lett. B 810, 135843 (2020), arXiv:2005.03859 [gr-qc]

    Pith/arXiv arXiv 2020

  42. [44]

    Magueijo and L

    J. Magueijo and L. Smolin, Class. Quant. Grav. 21, 1725 (2004), arXiv:gr-qc/0305055

    Pith/arXiv arXiv 2004

  43. [45]

    Nojiri and S

    S. Nojiri and S. D. Odintsov, Int. J. Geom. Meth. Mod. Phys. 4, 115 (2007), arXiv:hep-th/0601213

    Pith/arXiv arXiv 2007

  44. [46]

    Atazadeh, Ann

    K. Atazadeh, Ann. Phys. 446, 169133 (2022)

    2022

  45. [47]

    Zwiebach, Phys

    B. Zwiebach, Phys. Lett. B 156, 315 (1985)

    1985

  46. [48]

    Amelino-Camelia, Int

    G. Amelino-Camelia, Int. J. Mod. Phys. D 11, 35 (2002), arXiv:gr- qc/0012051

    arXiv 2002

  47. [49]

    Lu and Y

    H. Lu and Y. Pang and C. N. Pope, Phys. Lett. B 809, 135717 (2020), arXiv:2003.11552 [gr-qc]

    Pith/arXiv arXiv 2020

  48. [50]

    Ling, JCAP 08, 017 (2007), arXiv:gr-qc/0609129

    Y. Ling, JCAP 08, 017 (2007), arXiv:gr-qc/0609129

    Pith/arXiv arXiv 2007

  49. [51]

    A. M. Awad, A. F. Ali and B. Majumder, JCAP 10, 052 (2013), arXiv:1308.4343 [gr-qc]

    Pith/arXiv arXiv 2013

  50. [52]

    A. F. Ali, Phys. Rev. D 89, 104040 (2014), arXiv:1402.5320 [hep-th]

    Pith/arXiv arXiv 2014

  51. [53]

    Weinberg,Cosmology, Oxford University Press, Oxford (2008)

    S. Weinberg,Cosmology, Oxford University Press, Oxford (2008). 24

    2008