Pith. sign in

REVIEW 5 major objections 3 minor 1 cited by

Power-Law and Logarithmic Entropy-Corrected Ricci Dark Energy in a Non-Flat FRW Universe with Viscous Interaction

T0 review · 5 major / 3 minor · reviewed 2026-08-05 · deepseek-v4-flash

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

Pith's one-line read Entropy-corrected Ricci dark energy models yield closed-form dynamics and five scalar-field counterparts.

desk verdict The power-law entropy-corrected Ricci dark energy results are invalidated by a dropped reciprocal in Eq. (25); the logarithmic version is better, but the paper is still a routine extension with a formal-only correspondence. read the letter →

arxiv 2508.21110 v3 pith:YY5XQ4CZ submitted 2025-08-28 gr-qc

Antonio Pasqua This is my paper · ORCID
classification gr-qc MSC 83F05 PACS 95.36.+x98.80.-k
keywords holographicdarkenergyRiccipower-lawentropycorrectionlogarithmicbulkviscosityinteractingdecelerationparameterChaplygingascorrespondence
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper extends the Ricci-scalar version of holographic dark energy by adding power-law and logarithmic entropy corrections, placing the resulting fluids in a non-flat universe with bulk viscosity and an interaction with dark matter. It derives closed expressions for the dark-energy equation of state, the deceleration parameter, and the evolution of the density parameter. It then shows that, by equating equations of state, both corrected models can be rewritten as each of five known dark-energy field models, giving explicit scalar-field potentials and kinetic terms. The point of the exercise is to turn quantum-gravity-motivated entropy corrections into concrete, testable cosmic dynamics.

What carries the argument

The load-bearing object is the Ricci-scalar holographic cutoff L = R^(−1/2), where R = 6(Ḣ + 2H² + k/a²), together with the two entropy-corrected energy densities built on it. The derivation chain has three steps: express R in terms of ρm, ρΛ, and ωΛ from the Friedmann equations; invert that relation to get ωΛ; and feed ωΛ back into the balance equations, using the interaction Q = 3b²H(ρm+ρΛ) and bulk viscosity ξ = ερΛ/H, to obtain q and Ω'_Λ. The correspondences are carried by the equation-of-state parameter alone: setting ω_Λ equal to each scalar-field model's EoS fixes that model's free parameters in terms of ρΛ, ΩΛ, Ωk, and the entropy-correction constants.

What would settle it

Evaluate the relation H' = 1 used in deriving Eq. (38) on the paper's own flat-limit solution a ∝ t^p with p = 6α/(12α−1). There H = p/t and dH/d(ln a) = −H, so H' = 1 is not the general relation. Re-deriving Eqs. (34)–(38) with a general H'(x) would show directly whether Eq. (38) survives.

Watch

Extended reading notes

Core claim

The paper claims that replacing the holographic infrared cutoff with the inverse Ricci scalar R^(−1/2) and adding entropy corrections produces two closed dark-energy fluids—power-law corrected Ricci dark energy (PLECRDE) and logarithmic corrected Ricci dark energy (LECRDE)—whose dynamics can be written in closed form. Combining these densities with the Friedmann, conservation, and interaction equations yields an equation-of-state parameter, a deceleration parameter, and the evolution of the density parameter for each model. By equating these equations of state to those of the GCG, MVCG, NMCG, Yang-Mills, and NLED models, the paper reconstructs the scalar-field kinetic terms, potentials, and

Load-bearing premise

The evolution equation for Ω'_Λ rests on the identification H' = a'/a = 1 in Eq. (39); if that relation is not exact for the expanding background, the central evolution result built on it does not follow.

Editorial extensions

If this is right

  • The PLECRDE and LECRDE models can be represented as GCG, MVCG, NMCG, Yang-Mills, and NLED dark-energy fluids, with explicit formulas for the model parameters in terms of the dark-energy density, ΩΛ, Ωk, and the entropy-correction parameters.
  • In a flat, dark-energy-dominated universe the entropy corrections vanish and both models reduce to ordinary Ricci dark energy, with ω_Λ = 1/3 − 1/(9α) + 3ε and q = 1 − 1/(6α) + 9ε/2.
  • The phantom regime opens for α < 1/12 and cosmic acceleration begins at α ≤ 1/6 in the flat limit, giving parameter windows that could be matched against observations.
  • Bulk viscosity shifts the equation-of-state parameter by +3ε and the deceleration parameter by +9ε/2 in that limit, so dissipative effects directly alter the predicted expansion history.
  • The Yang-Mills and nonlinear-electrodynamics correspondences impose flat-limit constraints α > 1/12 and α ≠ −1/12 respectively.

Reading between the lines

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

  • A testable extension, not made in the paper, would be to fit the flat-limit constant equation of state to supernova and BAO data to see which α ranges remain viable and whether the entropy corrections are observationally distinguishable from a bare cosmological constant.
  • Because the EoS-equating procedure is independent of the cutoff choice in form, it could be applied to event-horizon or particle-horizon versions of entropy-corrected holographic dark energy; the paper does not do this.
  • Because ε and b² enter the flat-limit equations additively, independent measurements of ω and q could in principle separate the viscosity contribution from the model parameter α.
  • Replacing the special relation H' = 1 used in deriving Ω'_Λ with a general H'(x) would produce a modified evolution equation; comparing the two versions on numerical backgrounds is a direct way to gauge how sensitive that result is to the simplifying identification.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

5 major / 3 minor

Summary. The paper extends the Ricci dark energy model by adding power-law and logarithmic entropy corrections, in a non-flat FRW universe with bulk viscosity and a dark-energy/dark-matter interaction. It derives the equation-of-state parameter (Eqs. 25–26), the deceleration parameter (Eqs. 42–43), and the evolution of the density parameter Ω'_Λ (Eq. 38). It then constructs formal correspondences with GCG, MVCG, NMCG, Yang–Mills, and NLED scalar-field models by equating equations of state. The paper also analyzes a flat, dark-energy-dominated limiting case.

Significance. If correct, the closed-form expressions would be a useful compendium for reconstructing dark-energy dynamics from entropy-corrected Ricci densities. The paper compiles a substantial body of relevant literature and the reconstruction strategy is standard. However, the central equations contain algebraic and dimensional errors that invalidate the main results, and the 'correspondences' are identities constructed by solving for the target-model parameters. The paper does not currently provide reliable new physical results.

major comments (5)
  1. [§II, Eq. (25)] The substitution of the PLECRDE density into Eq. (24) is algebraically wrong. Eq. (24) contains RM_p^2/(3ρΛ); with ρΛ=3αM_p^2R−βM_p^2R^{γ/2} this equals 1/[3(3α−βR^{γ/2−1})], not (1/3)(3α−βR^{γ/2−1}) as written in Eq. (25). The reciprocal is dropped. This error propagates into Eq. (42), Eq. (38) (PLECRDE branch), and all Section III PLECRDE formulas. Consistency check: with β=0, Ωk=Ωm=0, Eq. (25) reduces to 3ε+1/3−α, whereas the paper's own flat limit, Eq. (50), gives 3ε+1/3−1/(9α); these agree only if α=1/3.
  2. [§II, Eq. (39) and Eq. (38)] Eq. (39) asserts H'=a'/a=1, identifying the derivative of H with respect to x=ln a with the derivative of the scale factor. In fact H'=dH/dx=Hdot/H. This identity is false in general. Consequently the step from Eq. (37) to Eq. (38), which removes H' by setting it to 1, is invalid. The claimed evolution equation for Ω'_Λ is therefore unsupported for both the PLECRDE and LECRDE models.
  3. [§II, Eq. (30)] The viscous term in Eq. (30) is dimensionally inconsistent. Eq. (18) has the term 9εHρΛ, with dimensions energy density × inverse time, matching the left side ρdotΛ. Eq. (30) instead writes 9H^2ερΛ, which has dimensions energy density × inverse time squared. This error propagates into Eq. (33) and into the subsequent derivation of Ω'_Λ, compounding the issue from Eq. (39).
  4. [§II, Eq. (42)] Independent of the error in Eq. (25), the substitution into Eq. (41) is algebraically inconsistent. Inserting Eq. (25) into q=(1/2)[1+Ωk+3ΩΛωΛ] gives q=1+Ωk+(9εΩΛ)/2 − (ΩΛ/2)(3α−βR^{γ/2−1}). Eq. (42) instead has −(1/2)ΩΛ/(3α−βR^{γ/2−1}), i.e. the reciprocal of the required term. Thus the PLECRDE deceleration parameter is not a valid consequence of the paper's own equations.
  5. [§III, Eqs. (67)–(68), (119), (148), (187), (203)] The 'correspondences' are constructed by equating the DE EoS parameter with each scalar-field model's EoS and then solving for that model's parameters, e.g. D=−ωΛρ^{θ+1} in Eq. (67), B0=a^{δ1}(A−ωΛ)ρ^{θ+1} in Eq. (119), A1=(ωΛ−B)ρ^{θ+1}a^{3(ωΛ+1)(θ+1)}/ωΛ in Eq. (148), and analogous inversions for y and B^2. These inversions are possible for any ωΛ, so the match is guaranteed by construction. The correspondences are formal identities rather than independent physical constraints. The Conclusions' statement that they 'reveal how different dark energy candidates are interrelated' overstates the result.
minor comments (3)
  1. [§II, Eq. (35)] For the record, Eq. (35) is correct: using Eq. (20) and Ωm+ΩΛ=1+Ωk gives R/(9H^2)=(2/3)(Hdot/H^2+2+Ωk). A concern that this equation misstates the Ricci-scalar relation does not land.
  2. [Introduction] There are several typographical issues, including 'fomr' for 'form' and inconsistent spacing in 'FR W'. The reference list also has missing DOIs for several entries.
  3. [§III.B, near Eq. (138)] The text 'δ=0' should presumably read 'δ1=0', since δ is not defined in the MVCG section; δ1 is the exponent introduced in Eq. (92).

Circularity Check

4 steps flagged · score 8.0 of 10

Section III 'correspondences' are tautological: for each scalar-field model the free parameter is solved from the PL/LECRDE EoS, so the match is guaranteed by construction.

  1. self definitional [Section III.A, Eqs. (55), (67), (69)]
    "ωΛ =− D / ρ^{θ+1}_Λ ⇒ D = −ω_Λ ρ^{θ+1}_Λ , (67) ... Using the R-PLECHDE EoS parameter ω_Λ,pl, we find D_pl = (ρ^{θ+1}_{Λ,pl}/3)[−3ε + 1/3(3α−βR^{γ/2−1}) − (1+Ω_k)/(3Ω_Λ)] . (69)"

    D is a free parameter of the GCG EoS p_D = −D/ρ_Λ^θ. Eq. (67) defines D to be whatever is needed so that the GCG EoS identically reproduces the input DE EoS ω_Λ. Eq. (69) is then just substitution of the previously obtained ω_Λ,pl into that definition. The 'correspondence' is therefore guaranteed by construction: any ω_Λ yields a D of this form. No independent content is added by 'finding' D_pl.

  2. self definitional [Section III.B, Eqs. (118)–(122)]
    "ωΛ = A − B0 a^{−δ1}/ρ^{θ+1}_Λ , (118) which gives B0 = a^{δ1}(A−ω_Λ)ρ^{θ+1}_Λ . (119) ... For the R-PLECHDE model, substituting ωΛ yields B0,pl = a^{δ1}[A−3ε + 1/3(3α−βR^{γ/2−1}) − (1+Ω_k)/(3Ω_Λ)] ρ^{θ+1}_{Λ,pl} , (122)"

    Same construction as GCG: B0 (and C) are free MVCG parameters solved from the MVCG EoS after setting ω_Λ equal to the DE EoS. The parameter is defined in terms of the very quantity it is supposed to match, so the correspondence is a tautology. The subsequent 'reconstruction' of φ˙² and V(φ) via φ˙²=(1+ω_Λ)ρ_Λ and V=(1−ω_Λ)ρ_Λ/2 is likewise the standard rewriting of any perfect fluid as a quintessence field, not a test.

2 more flagged steps
  1. self definitional [Section III.C, Eqs. (143), (147)–(150)]
    "K(a)=−ω_Λ A1 a^{−3(ω_Λ+1)(θ+1)} (144) ... A1 = (ω_Λ − B)/ω_Λ ρ^{θ+1}_Λ a^{3(ω_Λ+1)(θ+1)} (148). For the R-PLECHDE model, inserting ω_Λ,pl gives A1,pl = ... (150)."

    A1 is the free parameter of the NMCG EoS; Eq. (148) solves for it by imposing ω_NMCG = ω_Λ. Thus the NMCG parameters are defined as functions of the very DE EoS they are said to reproduce. The matching is automatic for any ω_Λ, making the 'correspondence' a restatement of the input.

  2. self definitional [Section III.D–E, Eqs. (184)–(188) and (201)–(203)]
    "ω_y = (y−3)/[3(y+1)] (184) ... y = −(3(ω_Λ+1))/(3ω_Λ−1) (187). For the R-PLECHDE model, we obtain y_pl = −(3(ω_Λ,pl+1))/(3ω_Λ,pl−1) (188). ... B^2 = (1−3ω_Λ)/[8µω(5−3ω_Λ)] (203)."

    For YM, Eq. (187) is the algebraic inverse of the one-parameter YM EoS Eq. (184); substituting ω_Λ,pl into this inverse is a definition of y, not a prediction of the YM model. For NLED, Eq. (203) is likewise obtained by solving Eq. (201) for B² after equating ω_NLED with ω_Λ. These 'correspondences' hold for any input EoS and cannot fail; they add no information about whether the PL/LECRDE model is actually a Yang–Mills or NLED condensate.

full rationale

The Section II derivation chain is not circular: it starts from assumed entropy-corrected Ricci energy densities, conservation equations, and the Friedmann equation, and algebraically derives ω_Λ, q, and Ω'_Λ. However, the central claim of Section III—'we establish a correspondence'—is circular in the specific sense of pattern 1. For each scalar-field model, the paper takes the model's EoS, sets it equal to the already-derived ω_Λ, and solves for that model's free parameter (D; B0, C; A1, B1; y; B²). For example, Eq. (67) defines D = −ω_Λ ρ^{θ+1}; Eq. (119) defines B0 = a^{δ1}(A−ω_Λ)ρ^{θ+1}; Eq. (187) is the inverse of the one-parameter YM EoS. These definitions guarantee the 'correspondence' for any input ω_Λ, so the resulting expressions (69), (122), (150), (188), (204) are substitutions, not predictions. The same applies to the reconstructed φ˙² and V. This makes the claimed interrelations vacuous by construction. The many self-citations (Refs. 41–50) are merely bibliographic and not load-bearing. The paper also contains serious algebraic errors—Eq. (25) drops the reciprocal of (3α−βR^{γ/2−1}), and Eq. (39) sets H'=1—but those are correctness issues, not circularity; they are noted here to separate them from the circularity finding. Overall, because the Section III 'correspondence' results are forced by definition, score = 8.

Assumptions & free parameters 8 free parameters · 7 assumptions · 0 invented entities

The central derivation rests on the holographic dark energy ansatz, the Ricci cut-off, and two quantum-entropy correction forms, all imported from prior literature. It also assumes phenomenological viscosity and interaction parameterizations. No new particles, forces, or fields are introduced. Many parameters (alpha, beta, gamma, gamma_1, gamma_2, epsilon, b^2, theta) remain free, and the scalar-field correspondences introduce additional free parameters.

free parameters (8)
  • alpha = approximately 0.46 (cited from Gao et al., not fit here)
    Multiplicative constant in rho_Lambda = 3 alpha M_p^2 R; controls phantom crossing and acceleration conditions.
  • beta
    Amplitude of the power-law entropy correction in Eq. (5).
  • gamma
    Exponent of the power-law correction R^{gamma/2} in Eq. (5).
  • gamma_1
    Coefficient of the R^2 log(M_p^2/R) term in Eq. (7).
  • gamma_2
    Coefficient of the R^2 term in Eq. (7).
  • epsilon
    Bulk viscosity coefficient in the parameterization xi = epsilon rho_Lambda H^{-1}.
  • b^2
    Dimensionless DE-DM interaction coupling in Q = 3 b^2 H (rho_m + rho_Lambda).
  • theta
    Exponent in the GCG, MVCG, and NMCG equations of state; appears throughout the correspondence section.
assumptions (7)
  • standard math FRW metric and Friedmann equations (Eqs. 8-9) describe the background spacetime.
    The background geometry and field equations are assumed without derivation.
  • domain assumption Holographic dark energy density rho_Lambda = 3 alpha M_p^2 L^{-2} saturates the black-hole entropy bound.
    The HDE ansatz is cited from Cohen, Kaplan, Nelson and Li, and is the starting point for the Ricci cut-off.
  • domain assumption The Ricci scalar curvature is used as the infrared cut-off, L = R^{-1/2}.
    Adopted from Gao et al. [32] to avoid causality problems and address the coincidence problem.
  • domain assumption The power-law and logarithmic entropy corrections, Eqs. (1)-(2), are valid forms of quantum-corrected entropy.
    These forms are taken from prior literature on entanglement entropy and loop quantum gravity.
  • domain assumption Bulk viscosity has the parameterization xi = epsilon rho_Lambda H^{-1}.
    The viscous contribution to the pressure is assumed to be -3 epsilon rho_Lambda, following the cited work of Karami et al.
  • domain assumption The DE-DM interaction term is Q = 3 b^2 H (rho_m + rho_Lambda).
    A phenomenological interaction form, widely used in the literature and adopted without derivation.
  • domain assumption The scalar field models (GCG, MVCG, NMCG, YM, NLED) have the equations of state quoted in Section III.
    The target models and their EoS forms are taken from the cited literature.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Power-Law and Logarithmic Entropy-Corrected Ricci Dark Energy in a Non-Flat FRW Universe with Viscous Interaction." pith.science (2026). https://pith.science/paper/YY5XQ4CZ

@misc{pith2026250821110,
  author       = {Pith},
  title        = {Pith review of: Power-Law and Logarithmic Entropy-Corrected Ricci Dark Energy in a Non-Flat FRW Universe with Viscous Interaction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YY5XQ4CZ}},
  note         = {Machine review of arXiv:2508.21110}
}
abstract

In this work, we consider the power-law corrected and the logarithmic-corrected versions of the Holographic Dark Energy (HDE) model in a non-flat FRW Universe filled with a viscous Dark Energy (DE) interacting with Dark Matter (DM). We propose to replace the infrared cut-off with the inverse of the Ricci scalar curvature $R$. We obtain the equation of state (EoS) parameter $\omega_{\Lambda}$, the deceleration parameter $q$ and the evolution of energy density parameter $\Omega_{\Lambda} '$ in the presence of interaction between DE and DM for both corrections. We study the correspondence of the power-law entropy corrected Ricci dark energy (PLECRDE) and the logarithmic entropy corrected Ricci dark energy (LECRDE) models with the Generalized Chaplygin Gas (GCG), the Modified Variable Chaplygin Gas (MVCG), the New Modified Chaplygin Gas (NMCG), the Yang-Mills (YM) and the Non Linear Electro-Dynamics (NLED) scalar field models.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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

  1. Scalar Field Reconstructions of Holographic Dark Energy Models with Applications to Chaplygin Gas, DBI, Yang-Mills, and NLED Frameworks

    gr-qc 2025-09 reject novelty 3.0 of 10

    A catalogue of analytic expressions equating two holographic dark energy models with Chaplygin gas, DBI, Yang-Mills and NLED scalar fields, built from standard reconstruction identities.

Reference graph

Works this paper leans on

105 extracted references · 57 canonical work pages · cited by 1 Pith paper

  1. [1]

    Riess et al., Astron

    A.G. Riess et al., Astron. J.116, 1009 (1998). DOI: 10.1086/300499

    doi:10.1086/300499 1998

  2. [2]

    Perlmutter et al., Astrophys

    S. Perlmutter et al., Astrophys. J.517, 565 (1999); http://supernova.lbl.gov/ DOI:10.1086/307221

    doi:10.1086/307221 1999

  3. [3]

    Tegmark et al., Phys

    M. Tegmark et al., Phys. Rev. D69, 103501 (2004). DOI: https://doi.org/10.1103/PhysRevD.69.103501

    doi:10.1103/physrevd.69.103501 2004

  4. [5]

    Spergel et al., Astrophys

    D.N. Spergel et al., Astrophys. J. Suppl.148, 175 (2003). DOI: https://doi.org/10.1086/377226

    doi:10.1086/377226 2003

  5. [6]

    Komatsu et al., Astrophys

    E. Komatsu et al., Astrophys. J. Suppl.180, 330 (2009). DOI: https://doi.org/10.1088/0067-0049/180/2/330

    doi:10.1088/0067-0049/180/2/330 2009

  6. [7]

    Padmanabhan, Phys

    T. Padmanabhan, Phys. Rept.380, 235 (2003). DOI: https://doi.org/10.48550/arXiv.hep-th/0212290

    arXiv doi:10.48550/arxiv.hep-th/0212290 2003

  7. [8]

    Sahni, Lect

    V. Sahni, Lect. Notes Phys.653, 141 (2004). DOI: https://doi.org/10.48550/arXiv.astro-ph/0403324

    arXiv doi:10.48550/arxiv.astro-ph/0403324 2004

  8. [9]

    Sahni, Class

    V. Sahni, Class. Quant. Grav.19, 3435 (2002). DOI: https://doi.org/10.1088/0264-9381/19/13/304

    doi:10.1088/0264-9381/19/13/304 2002

Show all 105 references
  1. [10]

    ’t Hooft, arXiv:gr-qc/9310026

    G. ’t Hooft, arXiv:gr-qc/9310026. DOI: https://doi.org/10.48550/arXiv.gr-qc/9310026

    doi arXiv

  2. [11]

    Cohen, D

    A. Cohen, D. Kaplan, A. Nelson, Phys. Rev. Lett.82, 4971 (1999). DOI: https://doi.org/10.1103/PhysRevLett.82.4971

    1999 doi

  3. [12]

    Li, Phys

    M. Li, Phys. Lett. B603, 1 (2004). DOI: https://doi.org/10.1016/j.physletb.2004.10.014

    2004 doi

  4. [13]

    Myung, Astrophys

    Y.S. Myung, Astrophys. Space Sci.335553-559, (2011). DOI: https://doi.org/10.1007/s10509-011-0753-3

    2011 doi

  5. [14]

    M. Li, X.D. Li, S. Wang, Y. Wang, X. Zhang, J. Cosmol. Astropart. Phys.12, 014 (2009). DOI: https://doi.org/10.1088/1475-7516/2009/12/014

    2009 doi

  6. [15]

    Khurshudyan, Astrophys

    M. Khurshudyan, Astrophys. Space Sci.361, 7 (2016). DOI:

    2016

  7. [16]

    Nojiri, S.D

    S. Nojiri, S.D. Odintsov, Gen. Rel. Grav.38, 1285 (2006). DOI:

    2006

  8. [17]

    Nojiri, S.D

    S.I. Nojiri, S.D. Odintsov, V.K. Oikonomou, T. Paul, Phys. Rev. D102, 023540 (2020). DOI:

    2020

  9. [18]

    Nojiri, S.D

    S. Nojiri, S.D. Odintsov, T. Paul, Symmetry13, 928 (2021). DOI:

    2021

  10. [19]

    S. Das, S. Shankaranarayanan, S. Sur, Phys. Rev. D77, 064013 (2008). DOI: https://doi.org/10.1103/PhysRevD.77.064013

    2008 doi

  11. [20]

    S. Das, S. Shankaranarayanan, S. Sur, arXiv:1002.1129. DOI: https://doi.org/10.48550/arXiv.1002.1129

    doi arXiv

  12. [21]

    S. Das, S. Shankaranarayanan, S. Sur, arXiv:0806.0402. DOI: https://doi.org/10.48550/arXiv.0806.0402

    doi arXiv

  13. [22]

    Radicella, D

    N. Radicella, D. Pavon, Phys. Lett. B691, 121 (2010). DOI: https://doi.org/10.1016/j.physletb.2010.06.019

    2010 doi

  14. [23]

    Sheykhi, M

    A. Sheykhi, M. Jamil, Gen. Rel. Grav.43, 2661 (2011). DOI: https://doi.org/10.1007/s10714-011-1190-x

    2011 doi

  15. [24]

    Banerjee, S.K

    R. Banerjee, S.K. Modak, JHEP0911, 073 (2009). DOI: https://doi.org/10.1088/1126-6708/2009/11/073

    2009 doi

  16. [25]

    Banerjee, R.K

    S. Banerjee, R.K. Gupta, A. Sen, JHEP1103, 147 (2011). DOI: https://doi.org/10.48550/arXiv.1005.3044

    2011 doi arXiv

  17. [26]

    Sadjadi, M

    H.M. Sadjadi, M. Jamil, Gen. Rel. Grav.43, 1759 (2011). DOI: DOI: https://doi.org/10.1007/s10714-011-1155-0

    2011 doi

  18. [27]

    Bamba, M

    K. Bamba, M. Jamil, D. Momeni, R. Myrzakulov, Astrophys. Space Sci.344, 259-267 (2013) . DOI: https://doi.org/10.1007/s10509-012-1312-2

    2013 doi

  19. [28]

    Nojiri, S.D

    S. Nojiri, S.D. Odintsov, V. Faraoni, Phys. Rev. D105, 044042 (2022). DOI: https://doi.org/10.1103/PhysRevD.105.044042

    2022 doi

  20. [29]

    Jamil, M.U

    M. Jamil, M.U. Farooq, JCAP03, 001 (2010). DOI: https://doi.org/10.1088/1475-7516/2010/03/001

    2010 doi

  21. [30]

    Karami, M

    K. Karami, M. Jamil, N. Sahraei, Phys. Scr.82, 045901 (2010). DOI: https://doi.org/10.1088/0031-8949/82/04/045901

    2010 doi

  22. [31]

    M. R. Setare, M. Jamil, Europhys. Lett.92, 49003 (2010). DOI: https://doi.org/10.1209/0295-5075/92/49003

    2010 doi

  23. [32]

    C. Gao, F. Wu, X. Chen, Y.-G. Shen, Phys. Rev. D79, 043511 (2009). DOI: https://doi.org/10.1103/PhysRevD.79.043511

    2009 doi

  24. [33]

    Duran, D

    I. Duran, D. Pavon, Phys. Rev. D83, 023504 (2011). DOI: 10.1103/PhysRevD.83.023504

    2011 doi

  25. [34]

    Zadeh, A

    M.A. Zadeh, A. Sheykhi, H. Moradpour, Eur. Phys. J. C78, 940 (2018). DOI: 10.1140/epjc/s10052-018-6427-3

    2018 doi

  26. [35]

    Zhang, Phys

    X. Zhang, Phys. Rev. D79, 103509 (2009). DOI: 10.1103/PhysRevD.79.103509

    2009 doi

  27. [36]

    Mathew, J

    T.K. Mathew, J. Suresh, D. Divakaran, Int. J. Mod. Phys. D22, 1350056 (2013). DOI: 10.1142/S0218271813500569

    2013 doi

  28. [37]

    S. Wang, Y. Wang, M. Li, Phys. Rep.696, 1–57 (2017). DOI: 10.1016/j.physrep.2017.06.003

    2017 doi

  29. [38]

    Zhang, H.Y

    J.F. Zhang, H.Y. Dong, J.Z. Qi, Eur. Phys. J. C80, 217 (2020). DOI: 10.1140/epjc/s10052-020-7767-3

    2020 doi

  30. [39]

    Malekjani, M

    M. Malekjani, M. Rezaei, I.A. Akhlaghi, Phys. Rev. D98, 063533 (2018). DOI: 10.1103/PhysRevD.98.063533

    2018 doi

  31. [40]

    T.F. Fu, J.F. Zhang, J.Q. Chen, Eur. Phys. J. C72, 1932 (2012). DOI: 10.1140/epjc/s10052-012-1932-2

    1932 doi

  32. [41]

    Pasqua, S

    A. Pasqua, S. Chattopadhyay, I. Khomenko, Can. J. Phys.91, 632 (2013). DOI: 10.1139/cjp-2013-0016

    2013 doi

  33. [42]

    Pasqua, M

    A. Pasqua, M. Jamil, R. Myrzakulov, B. Majeed, Phys. Scripta86, 045004 (2012). DOI: 10.1088/0031-8949/86/04/045004

    2012 doi

  34. [43]

    Pasqua, I

    A. Pasqua, I. Khomenko, Int. J. Theor. Phys.52, 3981 (2013). DOI: 10.1007/s10773-013-1711-3

    2013 doi

  35. [44]

    Chattopadhyay, A

    S. Chattopadhyay, A. Pasqua, Eur. Phys. J. Plus129, 31 (2014). DOI: 10.1140/epjp/i2014-14031-5

    2014 doi

  36. [45]

    Pasqua, S

    A. Pasqua, S. Chattopadhyay, I. Radinschi, A.A. Alshehri, A.N. Tawfik, Annals Phys.465, 169685 (2024). DOI: 10.1016/j.aop.2024.169685

    2024

  37. [46]

    Pasqua, S

    A. Pasqua, S. Chattopadhyay, M. Khurshudyan, R. Myrzakulov, M. Hakobyan, A. Movsisyan, Int. J. Theor. Phys.54, 972 (2015). DOI: 10.1007/s10773-015-2671-2 23

    2015 doi

  38. [47]

    Chattopadhyay, A

    S. Chattopadhyay, A. Pasqua, Can. J. Phys.92, 200 (2014). DOI: 10.1155/2013/251498

    2014 doi

  39. [48]

    Pasqua, K.A

    A. Pasqua, K.A. Assaf, A.A. Aly, Int. J. Theor. Phys.53, 566 (2014). DOI: https://doi.org/10.1007/s10773-013-1841-7

    2014 doi

  40. [49]

    Pasqua, S

    A. Pasqua, S. Chattopadhyay, M. Khurshudyan, et al., Int. J. Theor. Phys.53, 2988 (2014). DOI: https://doi.org/10.1007/s10773-014-2096-7

    2014 doi

  41. [50]

    Pasqua, Astrophys

    A. Pasqua, Astrophys. Space Sci.346, 531 (2013). DOI: https://doi.org/10.1007/s10509-013-1464-8

    2013 doi

  42. [51]

    Spergel et al., Astrophys

    D.N. Spergel et al., Astrophys. J. Suppl.170, 377 (2007). DOI: 10.1086/513700

    2007 doi

  43. [52]

    Ren, X.-H

    J. Ren, X.-H. Meng, Phys. Lett. B633, 1 (2006). DOI: https://doi.org/10.1016/j.physletb.2005.11.055

    2006 doi

  44. [53]

    Ren, X.-H

    J. Ren, X.-H. Meng, Phys. Lett. B636, 5 (2006). DOI: https://doi.org/10.1016/j.physletb.2006.03.029

    2006 doi

  45. [54]

    Tanmoy Paul Phys. Rev. D1118, 083540 (2025). DOI: 10.1103/PhysRevD.111.083540

    2025 doi

  46. [55]

    Karami, A

    K. Karami, A. Abdolmaleki, N. Sahraei, S. Ghaffari, JHEP1108, 150 (2011). DOI: https://doi.org/10.48550/arXiv.1009.3833

    2011 doi arXiv

  47. [56]

    Sheykhi, M.R

    A. Sheykhi, M.R. Setare, Int. J. Theor. Phys.49, 2777 (2010). DOI: https://doi.org/10.1007/s10773-010-0469-0

    2010 doi

  48. [57]

    Farooq, M

    M.U. Farooq, M. Jamil, U. Debnath, Astrophys. Space Sci.334, 243 (2011). DOI: https://doi.org/10.1007/s10509-011- 0721-y

    2011 doi

  49. [58]

    Karami, M.S

    K. Karami, M.S. Khaledian, M. Jamil, Phys. Scr.83, 025901 (2011). DOI: https://doi.org/10.1088/0031- 8949/83/02/025901

    2011 doi

  50. [59]

    Sheykhi, M

    A. Sheykhi, M. Jamil, Phys. Lett. B694, 284 (2011). DOI: https://doi.org/10.1016/j.physletb.2010.10.019

    2011 doi

  51. [60]

    Sheykhi, K

    A. Sheykhi, K. Karami, M. Jamil, E. Kazemi, M. Haddad, Gen. Relativ. Grav.44, 623 (2012). DOI: https://doi.org/10.1007/s10714-011-1315-2

    2012 doi

  52. [61]

    Karami, A

    K. Karami, A. Sheykhi, M. Jamil, Z. Azarmi, M.M. Soltanzadeh, Gen. Relativ. Grav.43, 27 (2011). DOI: https://doi.org/10.1007/s10714-010-1072-7

    2011 doi

  53. [62]

    Jamil, E.N

    M. Jamil, E.N. Saridakis, JCAP1007, 028 (2010). DOI: https://doi.org/10.1088/1475-7516/2010/07/028

    2010 doi

  54. [63]

    Jamil, M.A

    M. Jamil, M.A. Rashid, Eur. Phys. J. C56, 429 (2008). DOI: https://doi.org/10.1140/epjc/s10052-008-0670-y

    2008 doi

  55. [64]

    Mazumder, R

    N. Mazumder, R. Biswas, S. Chakraborty, arXiv:1106.4627v2 [gr-qc]. DOI: https://doi.org/10.48550/arXiv.1106.4627

    doi arXiv

  56. [65]

    Jamil, M.A

    M. Jamil, M.A. Rashid, Eur. Phys. J. C60, 141 (2009). DOI: 10.1140/epjc/s10052-009-0869-6

    2009 doi

  57. [66]

    Baldi, P

    M. Baldi, P. Salucci, JCAP02014 (2012). DOI: 10.1088/1475-7516/2012/02/014

    2012 doi

  58. [67]

    Marulli, M

    F. Marulli, M. Baldi, L. Moscardini, Mon. Not. R. Astron. Soc.420, 2377 (2012). DOI: https://doi.org/10.1111/j.1365- 2966.2011.20199.x

    2012

  59. [68]

    Clemson, K

    T. Clemson, K. Koyama, G.-B. Zhao, R. Maartens, J. Valiviita, Phys. Rev. D85, 043007 (2012). DOI: https://doi.org/10.1103/PhysRevD.85.043007

    2012 doi

  60. [69]

    Solano, U

    F.C. Solano, U. Nucamendi, arXiv:1109.1303v2 [astro-ph.CO]. DOI: https://doi.org/10.48550/arXiv.1109.1303

    doi arXiv

  61. [70]

    S. Cao, N. Liang, Z.-H. Zhu, arXiv:1012.4879v3 [astro-ph.CO]. DOI: https://doi.org/10.48550/arXiv.1012.4879

    doi arXiv

  62. [71]

    J.-H. He, B. Wang, E. Abdalla, Phys. Rev. D83, 063515 (2011). DOI: https://doi.org/10.1103/PhysRevD.83.063515

    2011 doi

  63. [72]

    Kamenshchik, U

    A. Kamenshchik, U. Moschella, V. Pasquier, Phys. Lett. B511, 265 (2001). DOI: https://doi.org/10.1016/S0370- 2693(01)00571-8

    2001 doi

  64. [73]

    M. Li, X. Li, X. Zhang, Sci. China Phys. Mech. Astron.53, 1631 (2010). DOI: https://doi.org/10.1007/s11433-010-4083-1

    2010 doi

  65. [74]

    Bento, O

    M.C. Bento, O. Bertolami, A.A. Sen, Phys. Rev. D70, 083519 (2004). DOI: https://doi.org/10.1103/PhysRevD.70.083519

    2004 doi

  66. [75]

    Gorini, A

    V. Gorini, A. Kamenshchik, U. Moschella, Phys. Rev. D67, 063509 (2003). DOI: https://doi.org/10.1103/PhysRevD.67.063509

    2003 doi

  67. [76]

    U. Alam, V. Sahni, T.D. Saini, A.A. Starobinsky, Mon. Not. R. Astron. Soc.344, 1057 (2003). DOI: https://doi.org/10.1046/j.1365-8711.2003.06871.x

    2003

  68. [77]

    Bento, O

    M.C. Bento, O. Bertolami, A.A. Sen, Phys. Rev. D66, 043507 (2002). DOI: https://doi.org/10.1103/PhysRevD.66.043507

    2002 doi

  69. [78]

    Bilic, G.B

    N. Bilic, G.B. Tupper, R.D. Viollier, Phys. Lett. B535, 17 (2002). DOI: https://doi.org/10.1016/S0370-2693(02)01716-1

    2002 doi

  70. [79]

    Fabris, S.B.V

    J.C. Fabris, S.B.V. Gon¸ calves, P.E. de Souza, Gen. Relativ. Grav.34, 53 (2002). DOI: https://doi.org/10.1023/A:1015266421750

    2002 doi

  71. [80]

    Gorini, A.Y

    V. Gorini, A.Y. Kamenshchik, U. Moschella, O.F. Piattella, A.A. Starobinsky, J. Cosmol. Astropart. Phys.2, 16 (2008). DOI: https://doi.org/10.1088/1475-7516/2008/02/016

    2008 doi

  72. [81]

    Zhang, J

    X. Zhang, J. Zhang, J. Cui, L. Zhang, Mod. Phys. Lett. A24, 1763 (2009). DOI: https://doi.org/10.1142/S0217732309021530

    2009 doi

  73. [82]

    Guo, Y.Z

    Z.K. Guo, Y.Z. Zhang, arXiv:astro-ph/0506091 (2005). DOI: https://doi.org/10.48550/arXiv.astro-ph/0506091

    2005 doi arXiv

  74. [83]

    Bento, O

    M.C. Bento, O. Bertolami, A.A. Sen, Phys. Lett. B575, 172 (2003). DOI: https://doi.org/10.1016/j.physletb.2003.08.017

    2003 doi

  75. [84]

    Sethi, S.K

    G. Sethi, S.K. Singh, P. Kumar, D. Jain, A. Dev, arXiv:astro-ph/0508491 (2005). DOI: https://doi.org/10.48550/arXiv.astro-ph/0508491

    2005 doi arXiv

  76. [85]

    Guo, Y.Z

    Z.K. Guo, Y.Z. Zhang, arXiv:astro-ph/0509790 (2005). DOI: https://doi.org/10.48550/arXiv.astro-ph/0509790

    2005 doi arXiv

  77. [86]

    Debnath, Astrophys

    U. Debnath, Astrophys. Space Sci.312, 295 (2007). DOI: https://doi.org/10.1007/s10509-007-9690-6

    2007 doi

  78. [87]

    Bertolami et al., Mon

    O. Bertolami et al., Mon. Not. R. Astron. Soc.353, 329 (2004). DOI: https://doi.org/10.1111/j.1365-2966.2004.08022.x

    2004

  79. [88]

    Tekola, arXiv:gr-qc/0706.0804 (2007)

    A.G. Tekola, arXiv:gr-qc/0706.0804 (2007). DOI: https://doi.org/10.48550/arXiv.gr-qc/0706.0804

    2007 doi arXiv

  80. [89]

    Chattopadhyay, U

    S. Chattopadhyay, U. Debnath, arXiv:0805.007v [gr-qc] (2008). DOI: https://doi.org/10.48550/arXiv.0805.007

    2008 doi

  81. [90]

    Zhang et al., JCAP01, 003 (2006)

    X. Zhang et al., JCAP01, 003 (2006). DOI: https://doi.org/10.1088/1475-7516/2006/01/003

    2006 doi

  82. [91]

    Zhang, Phys

    Y. Zhang, Phys. Lett. B340, 18 (1994). DOI: https://doi.org/10.1016/0370-2693(94)91291-2

    1994 doi

  83. [92]

    T.Y. Xia, Y. Zhang, Phys. Lett. B656, 19 (2007). DOI: https://doi.org/10.1016/j.physletb.2007.09.029

    2007 doi

  84. [93]

    M. Tong, Y. Zhang, T. Xia, Int. J. Mod. Phys. D18, 797 (2009). DOI: https://doi.org/10.1142/S0218271809014765

    2009 doi

  85. [94]

    W. Zhao, Y. Zhang, Class. Quant. Grav.23, 3405 (2006). DOI: 10.1088/0264-9381/23/10/011

    2006 doi

  86. [95]

    Zhao, Astron

    W. Zhao, Astron. Astrophys.9, 874 (2009). DOI: 10.1088/1674-4527/9/8/003 24

    2009 doi

  87. [96]

    Politzer, Phys

    H. Politzer, Phys. Rev. Lett.30, 1346 (1973). DOI: https://doi.org/10.1103/PhysRevLett.30.1346

    1973 doi

  88. [97]

    Gross, F

    D.J. Gross, F. Wilczek, Phys. Rev. Lett.30, 1343 (1973). DOI: https://doi.org/10.1103/PhysRevLett.30.1343

    1973 doi

  89. [98]

    Adler, Phys

    S.L. Adler, Phys. Rev. D23, 2905 (1981). DOI: https://doi.org/10.1103/PhysRevD.23.2905

    1981 doi

  90. [99]

    Adler, Nucl

    S.L. Adler, Nucl. Phys. B217, 3881 (1983). DOI: https://doi.org/10.1016/0550-3213(83)90274-5

    1983 doi

  91. [100]

    Pagels, E

    H. Pagels, E. Tomboulis, Nucl. Phys. B143, 485 (1978). DOI: https://doi.org/10.1016/0550-3213(78)90065-2

    1978 doi

  92. [101]

    Coleman, E

    S. Coleman, E. Weinberg, Phys. Rev. D7, 1888 (1973). DOI: https://doi.org/10.1103/PhysRevD.7.1888

    1973 doi

  93. [102]

    Parker, A

    L. Parker, A. Raval, Phys. Rev. D60, 063512 (1999). DOI: https://doi.org/10.1103/PhysRevD.60.063512

    1999 doi

  94. [103]

    Copeland, A.R

    E.J. Copeland, A.R. Liddle, D. Wands, Phys. Rev. D57, 4686 (1989). DOI: https://doi.org/10.1103/PhysRevD.57.4686

    1989 doi

  95. [104]

    Barreiro, E.J

    T. Barreiro, E.J. Copeland, N.J. Nunes, Phys. Rev. D61, 127301 (2002). DOI: https://doi.org/10.1103/PhysRevD.61.127301

    2002 doi

  96. [105]

    Breton, R

    N. Breton, R. Garcia-Salcedo, arXiv:hep-th/0702008 . DOI: https://doi.org/10.48550/arXiv.hep-th/0702008

    doi arXiv

  97. [106]

    De Lorenci et al., Phys

    V.A. De Lorenci et al., Phys. Rev. D65, 063501 (2002). DOI: https://doi.org/10.1103/PhysRevD.65.063501

    2002 doi

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.