Comprehensive Study of Generalized Ghost Dark Energy in $f(\textsl{Q}, \textsl{L}_{m})$ Gravity: New Insights into Cosmic Dynamics

Baiju Dayanandan; M.Sharif; M. Zeeshan Gul; Shan Ali Qureshi

REVIEW 3 major objections 4 minor 71 references

Comprehensive Study of Generalized Ghost Dark Energy in $f(\textsl{Q}, \textsl{L}_{m})$ Gravity: New Insights into Cosmic Dynamics

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read This paper claims that generalized ghost dark energy in $f(Q,L_m)$ gravity, reconstructed from the density ansatz $\mu_D=\alpha H+\beta H^2$, yields a phantom-like, stable, observationally consistent late-time cosmic acceleration.

desk verdict The paper divides by f_Lm to define density and pressure, then reconstructs an f that has no L_m dependence, so the model is singular and its viability claims don't hold. read the letter →

arxiv 2501.01177 v1 pith:YA3H63FB submitted 2025-01-02 gr-qc

M. Zeeshan Gul , M.Sharif , Shan Ali Qureshi , Baiju Dayanandan This is my paper · ORCID

classification gr-qc PACS 95.36.+x98.80.-k04.50.Kd

keywords f(QLm)gravitygeneralizedghostdarkenergyreconstructionnon-metricityscalarcosmicevolutionstatefinderdiagnosticssquaredsoundspeed

topics Dark Energy Dark Matter

open problems Dark Matter 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

This paper tries to show that the generalized ghost dark energy model, with energy density $\mu_D = \alpha H + \beta H^2$, can be embedded in $f(Q,L_m)$ gravity, a modified theory built from the non-metricity scalar $Q$ and the matter Lagrangian $L_m$, and that the resulting reconstructed model describes the observed late-time acceleration. By choosing the matter Lagrangian as pressure, the authors solve for a specific functional form $f(Q,L_m)$ and then evaluate the dark-energy density, pressure, equation of state, statefinder pair, and squared sound speed. They report positive energy density, negative pressure, a phantom-like equation of state near $\omega_D=-1$, a Chaplygin-like $(r,s)$ trajectory, and $v_s^2>0$, and they take these as evidence that the model is stable and consistent with recent observational bounds on $\omega_D$. If the claim holds, modified gravity with non-metricity and matter coupling offers an alternative to the cosmological constant for the dark-energy sector.

What carries the argument

The load-bearing object is the reconstructed function $f(Q,L_m)=-\frac{\alpha c_1\sqrt{Q}(\ln Q+2)}{2\sqrt6}-\frac13\beta c_1 Q$, obtained by inserting the generalized ghost dark energy density $\mu_D=\alpha H+\beta H^2$ into the $f(Q,L_m)$ field equations for a flat FRW universe with interacting dark components. Here $Q$ is the non-metricity scalar, equal to $6H^2$ in this geometry, and $L_m$ is the matter Lagrangian. This function carries the argument: all subsequent densities, pressures, equation-of-state curves, statefinder pairs, and squared sound speeds are evaluations of the formulas built from it, with the redshift parametrization $H=H_0(1+z)^{1+q}$ connecting the model to observables.

What would settle it

Take the reconstructed function in Eq. (41) and compute $\partial f/\partial L_m$: because the function contains no $L_m$, this derivative is identically zero, while Eqs. (33) and (34), and therefore the quoted $\mu_D$, $P_D$, $\omega_D$, and $v_s^2$, all divide by $f_{L_m}$. That single calculation settles whether the presented reconstruction is well-defined, and it would force the model to be re-derived from a function with explicit $L_m$ dependence.

Watch

Extended reading notes

Core claim

On its own terms, the paper's discovery is a reconstruction: starting from the generalized ghost dark energy density $\mu_D=\alpha H+\beta H^2$ in a flat FRW universe with interacting dark energy and dark matter, the authors derive the field equations of $f(Q,L_m)$ gravity and invert them to obtain $f(Q,L_m)=-\frac{\alpha c_1\sqrt{Q}(\ln Q+2)}{2\sqrt6}-\frac13\beta c_1 Q$. Inserting this function into their expressions for dark-energy density and pressure, and using $H=H_0(1+z)^{1+q}$ with $q\approx -0.832$, yields $\mu_D=\alpha\sqrt{H_0^2(1+z)^{2+2q}}+\beta H_0^2(1+z)^{2+2q}$ and $P_D=-\mu_D$. From there the paper reports a phantom regime in the $\omega_D$ diagnostic, a freezing-region pattern in $(\omega_D,\omega'_D)$, a Chaplygin-gas statefinder pair, positive squared sound speed, and consistency with the dark-energy equation-of-state values quoted from recent observations.

Load-bearing premise

The derivation requires the derivative of $f$ with respect to the matter Lagrangian $L_m$ to be nonzero, but the reconstructed $f$ in Eq. (41) has no $L_m$ term, so that derivative is identically zero and the formulas built on it are not well defined.

Editorial extensions

If this is right

If the reconstruction is sound, symmetric teleparallel $f(Q,L_m)$ gravity can generate late-time acceleration without a cosmological constant.
The predicted phantom-like equation of state near $\omega_D=-1$ falls inside the observationally favored range, making the model a candidate alternative to $\Lambda$CDM.
Positive $v_s^2$ indicates that the background is stable to small perturbations, which would permit using the model for growth-of-structure calculations.
The Chaplygin-like $(r,s)$ trajectory gives a geometric signature that future distance measurements could use to distinguish this model from $\Lambda$CDM.

Reading between the lines

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

Beyond the paper, the close agreement between the reconstructed density and pressure and the input ansatz suggests that part of the phantom behavior is inherited from the assumed $\mu_D=\alpha H+\beta H^2$ rather than from the $f(Q,L_m)$ dynamics.
Beyond the paper, a natural correction is to add an explicit $L_m$-dependent piece to the reconstructed $f$ so that the derivative $f_{L_m}$ is nonzero, and then check whether the positive sound speed and phantom equation of state survive the re-derivation.
Beyond the paper, the phantom phase raises the question of a future singularity; evolving the model beyond $z=0$ would show whether it ends in a big rip or relaxes to de Sitter.
Beyond the paper, the same reconstruction route could be applied to holographic or pilgrim dark-energy densities to see whether the Chaplygin-like statefinder and stability are generic features of $f(Q,L_m)$ reconstructions.

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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

Dear [Name],

This one has a load-bearing problem that undermines its central claim. The reconstructed f(Q,L_m) in Eq. (41) is independent of L_m, so f_Lm = 0. But the energy density and pressure in Eqs. (33)-(34) are defined by dividing by f_Lm. The model as written is singular; you cannot divide by a derivative that vanishes identically. The stress-test note is correct, and it lands.

What is new: the exact combination of generalized ghost dark energy with f(Q,L_m) reconstruction does not appear in the cited literature. The paper is organized in the standard reconstruction-template way, and it computes the usual diagnostic quantities (EoS, statefinders, squared sound speed) mechanically. The reference list is extensive, though heavily self-cited.

The soft spots are not minor. First, the reconstruction step itself uses Eq. (33) which contains f_Lm in the denominator; solving for f with f_Lm = 0 is internally inconsistent. Everything downstream—Eqs. (42)-(43), the figures, the stability claim—inherits that problem. Second, Eq. (48) for \dot{H} is dimensionally wrong: it has units of H rather than H^2. The correct expression would involve H0^2(1+q)U^{2+2q}. Third, the EoS in Eq. (54) is not derived from the reconstructed μ_D and P_D; those give P_D = -μ_D, hence ω_D = -1 identically. The phantom behavior shown in Fig. 3 comes from a separate formula (Eq. 38) that depends on the ad hoc interaction parameter and the hand-picked α, β, c1, η. So the "predictions" are parameter-driven, not consequences of the model. Finally, the paper claims alignment with observational data but uses no data; the Planck values are just quoted.

In short, the paper does routine work in a crowded subfield and gets the central reconstruction wrong. I would not send it to peer review; a desk reject is appropriate. If the authors want to pursue this, they need to choose a functional form that genuinely depends on L_m and redo the reconstruction from Eq. (40).

Best regards.

Referee Report

3 major / 4 minor

Summary. The manuscript studies a generalized ghost dark energy (GGDE) model in f(Q,L_m) gravity. It derives the f(Q,L_m) field equations for a flat FRW universe, assumes a power-law scale factor, adopts the GGDE density ansatz μ_D = αH + βH^2, reconstructs the function f(Q,L_m), and then analyzes the resulting energy density, pressure, equation-of-state parameter, (ω_D, ω'_D)-plane, statefinder pair, and squared sound speed. The paper concludes that the reconstructed model produces positive energy density, negative pressure, phantom-like equation of state, Chaplygin-like statefinder behavior, and positive squared sound speed, and that these results are consistent with recent observational data.

Significance. If the reconstruction were valid, the paper would provide a concrete f(Q,L_m) realization of the GGDE model with second-order field equations and a complete set of cosmological diagnostics. The manuscript is organized and self-contained in its derivation of the non-metricity variation in the appendices, and it covers standard diagnostic tools. However, the central reconstruction is internally inconsistent: the reconstructed f(Q,L_m) in Eq. (41) has no L_m dependence, so f_{L_m}=0 identically, while Eqs. (33), (34), and (40) all divide by f_{L_m}. The density, pressure, and all derived quantities are therefore not well defined for the very model the paper claims to have constructed. In addition, the redshift-space mapping in Eq. (48) is dimensionally inconsistent, and the claimed predictions are largely algebraic consequences of the assumed μ_D ansatz. I do not regard the reported viability as established.

major comments (3)

[Section 2.1, Eqs. (33)–(41)] The reconstructed function in Eq. (41), f(Q,L_m) = -αc1√Q(ln Q + 2)/(2√6) - βc1 Q/3, contains no L_m term, so f_{L_m}=0 identically. Equations (33), (34), and (40) all divide by f_{L_m}. Therefore Eq. (40) cannot be used to determine f, and the expressions for μ_D, P_D, and every quantity derived from them, including Eqs. (42)–(63) and Figures 1–6, are not defined for this model. This is an internal inconsistency in the central reconstruction, not merely a disagreement with current observational constraints.
[Section 2.1, Eq. (48)] The second relation in Eq. (48) is dimensionally inconsistent. From H = H0 U^{1+q} with U = 1+z, one obtains ˙H = -(1+q) H0^2 U^{2+2q}, not -H0 U^{2+2q}. The missing factor (1+q) and the missing power of H0 affect the redshift-space form of ˙H used in Eq. (43) and therefore propagate into the pressure, equation-of-state, and stability results. The relation should be corrected and the subsequent formulas recomputed.
[Section 2.1, Eqs. (39), (42), and (52); Section 4] The claimed dark-energy predictions are largely algebraic consequences of the assumed ansatz. With Q = 6H^2, Eq. (42) reduces exactly to μ_D = αH + βH^2, which is Eq. (39), and Eq. (52) gives P_D = -μ_D by construction. The equation-of-state, statefinder, and sound-speed expressions are therefore controlled by the input ansatz and the selected parameters α = 1.5, β = 6.5, c1 = 0.4, and η near -0.95. The abstract and Section 4 present these as new dynamical predictions; the paper should at least acknowledge that they are built into the reconstruction.

minor comments (4)

[Section 2.1, Eq. (34)] The notation f_L and f_QL in Eq. (34) is not defined; if these denote partial derivatives, please define them explicitly.
[Section 2.1, Eqs. (37) and (39)] The symbol β is used for two different quantities: the energy-density ratio μ_m/μ_D in Eq. (37) and the GGDE coefficient in Eq. (39). This makes formulas such as Eq. (53) ambiguous.
[Section 2.1, Eqs. (21) and (24)] There are editorial glitches: Eq. (21) contains the citation '[6, ?]', Eq. (24) has an unbalanced parenthesis, and the sentence beginning 'We consider Substituting these values...' in Section 2.1 is incomplete.
[Figures 3 and 4] The axis labels and legends in Figures 3 and 4 are corrupted, including the legend entries for η in Figure 3 and the LaTeX in the ordinate of Figure 4, which prevents the reader from extracting the stated parameter values.

Circularity Check

2 steps flagged · score 7.0 of 10

The reconstructed model returns the assumed GGDE density by construction, and the reconstructed f has f_Lm = 0, so the central viability claims reduce to the input ansatz.

fitted input called prediction [Sec. 2.1, Eqs. (39)-(41), (51)-(52)]
"In this context, the energy density of the GGDE model is represented as µD = αH + βH^2. (39) Using Eqs.(33) and (39), we have [−12H^2 f_Q − L_m f_L + f]/f_L = αH + βH^2. (40) ... Substituting Eq.(49) in (42) and (43), we have µD = α√(H0^2 U^{2q+2}) + βH0^2U^{2q+2}, (51) PD = −α√(H0^2 U^{2q+2}) − βH0^2U^{2q+2}. (52)"

The reconstruction solves Eq. (40), which is exactly the condition that Eq. (33) equal the assumed GGDE density µD = αH + βH^2. With Q = 6H^2 and H = H0 U^{1+q}, Eq. (51) reduces to αH + βH^2, i.e., the input is returned unchanged, and Eq. (52) is its negative. All later diagnostics—phantom EoS, freezing region, Chaplygin-like statefinder pair, positive squared sound speed—are algebraic functions of this same assumed µD and the chosen parameters α = 1.5, β = 6.5, η ≈ −0.95. They therefore do not constitute an independent prediction of the f(Q,L_m) field equations.
other [Sec. 2, Eqs. (33)-(34); Sec. 2.1, Eq. (41)]
"µD and PD represent the energy density and pressure corresponding to DE expressed as µD = −12H2fQ − LmfLm + f / fL, (33) ... f(Q,Lm) = −αc1√Q(ln(Q)+2)/(2√6) − (1/3)βc1Q, (41)"

The reconstructed f in Eq. (41) contains no L_m term, so f_{L_m} = 0 identically. The definitions (33)-(34) from which the model's density and pressure are supposedly read divide by f_{L_m}. For this model those formulas are singular, so the finite expressions (42)-(43) and (51)-(52) cannot be obtained by substituting Eq. (41) into Eqs. (33)-(34). The reported quantities are the assumed ansatz reintroduced after a formally undefined division, which is a break in the derivation chain rather than an independent derivation.

full rationale

The paper is self-contained algebraically and does not rely on a load-bearing self-citation or imported uniqueness theorem, so the self-citation patterns do not drive the score. The circularity is in the reconstruction loop: Eq. (40) is obtained by equating the generalized density (33) to the assumed GGDE form (39), and the reconstructed f is then inserted to recover exactly that same form in Eq. (51). The EoS, statefinder, and sound-speed results are functions of this assumed µD and of hand-picked α, β, η; the asserted agreement with Planck's phantom ω_D is therefore a consequence of parameter choice, consistent with the paper's own Data Availability Statement that no data were used. In addition, the reconstructed f has ∂f/∂L_m = 0, so the denominators in Eqs. (33)-(34) vanish for the model actually presented; the finite expressions quoted in Eqs. (42)-(43) and (51)-(52) are not well-defined evaluations of those field-equation formulas. These two features make the central viability claim—positive density, negative pressure, phantom EoS, Chaplygin-like statefinders, stability—forced by the input ansatz rather than derived from first principles. Score 7 reflects substantial, central circularity, while not all algebraic steps (e.g., the explicit statefinder formulas) are themselves empty.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

No new particle, force, or geometric entity is introduced. The reconstruction relies instead on six free parameters or hand-chosen constants, a power-law background assumption, the L_m = p convention, and the GGDE density ansatz. The central derivation additionally requires f_Lm to be nonzero while the reconstructed f has no L_m dependence, which is an unresolved internal inconsistency.

free parameters (6)

alpha (GGDE linear coefficient) = 1.5 in all figures
Entered through the ansatz Eq.(39) and chosen by hand. No derivation or fit is provided.
beta (GGDE quadratic coefficient) = 6.5 in all figures
Same ansatz Eq.(39). The paper also uses beta as a density ratio in Eq.(37), creating a notation conflict.
eta (interaction coupling) = -0.95, -0.9501, -0.9502 in Fig.3
Chosen in a narrow band to place omega_D near the Planck phantom range. No uncertainty or fitting procedure is given.
c1 (integration constant) = 0.4 in figures
Integration constant from solving Eq.(40). Its value is arbitrary in the text.
q (deceleration parameter) = -0.832 taken from reference [64]
Used to set the power-law scale factor in Eqs.(44)-(46) and assumed constant over all redshifts, with no error propagation.
H0 (Hubble constant) = not specified
H0 appears in the redshift expressions and in all quantitative plots, but its value and units are never stated.

assumptions (5)

domain assumption Flat FRW metric with an ideal fluid stress-energy tensor
Used in Eqs.(29)-(30) to reduce the f(Q,L_m) field equations to the Friedmann-like equations.
ad hoc to paper The matter Lagrangian equals the pressure, L_m = p
Stated before Eq.(40). This is a common but non-unique choice and is required for the reconstruction.
ad hoc to paper Power-law scale factor a(t) = a0 t^k with constant deceleration q
Eqs.(44)-(46). This assumes a constant q across the entire redshift range, ignoring matter-radiation transitions.
ad hoc to paper GGDE energy density ansatz mu_D = alpha H + beta H^2
Eq.(39). This is the input that the reconstruction is built to reproduce, rather than a derived result.
domain assumption Interaction term Gamma = 3 eta H (mu_D + mu_m)
Eq.(36). A standard phenomenological interaction form, but eta is a free parameter.

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Cite this review

Pith. "Pith review of Comprehensive Study of Generalized Ghost Dark Energy in $f(\textsl{Q}, \textsl{L}_{m})$ Gravity: New Insights into Cosmic Dynamics." pith.science (2026). https://pith.science/paper/YA3H63FB

@misc{pith2026250101177,
  author       = {Pith},
  title        = {Pith review of: Comprehensive Study of Generalized Ghost Dark Energy in $f(\textslQ, \textslL_m)$ Gravity: New Insights into Cosmic Dynamics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YA3H63FB}},
  note         = {Machine review of arXiv:2501.01177}
}

abstract

This paper explores the generalized ghost dark energy model in the framework of $f(\textsl{Q}, \textsl{L}_{m})$ gravity, where $\textsl{Q}$ represents the non-metricity scalar and $\textsl{L}_{m}$ denotes the matter-Lagrangian density. We take the homogeneous and isotropic universe with an ideal matter distribution and examine a scenario with interacting dark energy and dark matter. We then reconstruct $f(\textsl{Q}, \textsl{L}_{m})$ model to examine the effects of this extended gravitational framework on the cosmic evolution. The behavior of numerous cosmic parameters are explored corresponding to distinct parametric values. The stability is evaluated by the squared sound speed method. The statefinder $(r,s)$ and standard diagnostic pairs $(\omega_D-\omega'_{D})$ are used to study the various cosmic eras. Our results align with recent observational evidence, indicating that the $f(\textsl{Q}, \textsl{L}_{m})$ model effectively characterizes dark energy and cosmic evolution.

Figures

Figures reproduced from arXiv: 2501.01177 by the authors.

**Figure 1.** Graph of f(Q, Lm) versus non-metricity and redshift for α = 1.5, β = 6.5 and c1 = 0.4. where the present deceleration parameter value is q = −0.832+0.091 −0.091 [64]. The relation for H and H0 is represented as H = ˙a a = 1 1 + q ( 1 t ), H0 = 1 1 + q ( 1 t0 ). (47) This signifies that the universe expansion is impacted by the deceleration parameter and H0. By computing the correlation between the redshift p… view at source ↗

**Figure 2.** Graphical representation of matter variables versus re [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗

**Figure 3.** Graph of ωD versus redshift for α = 1.5, β = 6.5 and c1 = 0.4. 3.1 Analysis of State Parameter The EoS parameter (ω = P µ ) represents correlation between energy density and pressure. This parameter helps to comprehend how these components impact cosmic dynamics. This parameter sheds light on the forces driving cosmic evolution and provides a more detailed understanding of the universe progression. Different values … view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: Plot of ωD versus ω ′ D for α = 1.5, β = 6.5 and c1 = 0.4. DE with the scalar field has been studied in [64]. Caldwell and Linder [65] classified DE frameworks into two different categories, i.e., the thawing region and the freezing region. In the thawing region, the …

**Figure 5.** Figure 5: Plot of r against s corresponding to α = 1.5, β = 6.5 and c1 = 0.4. × U6q+6)(36(H 2 0U 2q+2) 3/2 (α(α + 2(β − 3)q H 2 0U2q+2) + (β − 6)βH 2 0U 2q+2)(α + (β + 6η) q H 2 0U2q+2))−1 . (61) [PITH_FULL_IMAGE:figures/full_fig_p018_5.png]

**Figure 6.** Figure 6: Graph of squared sound speed versus redshift function [PITH_FULL_IMAGE:figures/full_fig_p020_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

71 extracted references · 47 canonical work pages

[1]

et al.: Astrophys

Swaters, R.A. et al.: Astrophys. J. 531(2000)107

work page 2000
[2]

and Starobinsky, A.A.: Int

Sahni, V. and Starobinsky, A.A.: Int. J. Mod. Phys. D 9(2000)373; Carroll, S.M.: Living Rev. Rel. 4(2001)1

work page 2000
[3]

and Odintsov, S.D.: Int

Nojiri, S.I. and Odintsov, S.D.: Int. J. Geom. Methods Mod. Phys. 4(2007)115

work page 2007
[4]

and Zhitnitsky, A.R.: Phys

Urban, F.R. and Zhitnitsky, A.R.: Phys. Rev. D 80(2009)063001

work page 2009
[5]

Ohta, N.: Phys. Lett. B 695(2011)41

work page 2011
[6]

et al.: Phys

Cai, R.G. et al.: Phys. Rev. D 84(2011)123501

work page 2011
[7]

and Movahed, M.S.: Gen

Sheykhi, A. and Movahed, M.S.: Gen. Relativ. Gravit. 44(2012)449

work page 2012
[8]

et al.: Mod

Feng, C.J. et al.: Mod. Phys. Lett. A 27(2012)1250182

work page 2012

Show all 71 references

[9]

and Shirafuji, T.: Phys

Hayashi, K. and Shirafuji, T.: Phys. Rev. D 19(1979)3524

1979
[10]

Linder, E.V.: Phys. Rev. D 81(2010)127301

2010
[11]

et al.: Phys

Jimenez, J.B. et al.: Phys. Rev. D 98(2018)044048

2018
[12]

Adeel, M.: et al.: Mod. Phys. Lett. A 38(2023)2350152

2023
[13]

Sharif, M.: et al.: Chin. J. Phys. 91(2024)66

2024
[14]

Rani, S.: et al.: Int. J. Geom. Methods Mod. Phys. 21(2024)2450033

2024
[15]

et.: Eur

Gul, M.Z. et.: Eur. Phys. J. C 84(2024)8

2024
[16]

et al.: Phys

Maurya, S.K. et al.: Phys. Dark Universe 46(2024)101619. 25

2024
[17]

109(2024)102211

Sharif, M.: et al.: New Astron. 109(2024)102211

2024
[18]

Dark Universe 47(2025)101754

Rani, S.: et al.: Phys. Dark Universe 47(2025)101754

2025
[19]

Dark Universe 47(2025)101760

Sharif, M.: et al.: Phys. Dark Universe 47(2025)101760

2025
[20]

High Energy Astrophys

Zhadyranova, A.: J. High Energy Astrophys. 44(2024)123

2024
[21]

et al.: Phys

Gul, M.Z. et al.: Phys. Scr. 99(2024)045006

2024
[22]

Koussour, M.: Chin. J. Phys. 90(2024)108

2024
[23]

et al.: Phys

Sharif, M. et al.: Phys. Scr. 99(2024)115003

2024
[24]

et al.: Chin

Gul, M.Z. et al.: Chin. Phys. C. 48(2024)12503

2024
[25]

Dark Universe 45(2024)101527

Koussour, M.: Phys. Dark Universe 45(2024)101527

2024
[26]

et al.: Chin

Gul, M.Z. et al.: Chin. J. Phys. 93(2025)256

2025
[27]

et al.: Phys

Nan, G. et al.: Phys. Dark Universe 46(2024)101635

2024
[28]

et al.: Eur

Gul, M.Z. et al.: Eur. Phys. J. C 84(2024)775; ibid 802; ibid 1232

2024
[29]

et al.: Mod

Sharif, M. et al.: Mod. Phys. Lett. A 39(2024)2450140

2024
[30]

et al.: Fortschr

Pradhan, S. et al.: Fortschr. der Phys. 72(2024)2400092

2024
[31]

et al.: Gen

Gul, M.Z. et al.: Gen. Relativ. Gravit. 56(2024)45

2024
[32]

et al.: Phys

Koussour, M. et al.: Phys. Dark Universe 46(2024)101577

2024
[33]

et al.: Chin

Gul, M.Z. et al.: Chin. J. Phys. 88(2024)388

2024
[34]

et al.: Eur

Sharif, M. et al.: Eur. Phys. J. C 84(2024)1094

2024
[35]

et al.: Phys

Myrzakulov, Y. et al.: Phys. Dark Universe 45(2024)101545

2024
[36]

and Gul, M.Z.: Ann

Sharif, M. and Gul, M.Z.: Ann. Phys. 465(2024)169674

2024
[37]

et al.: Physics of the Dark Universe 46(2024)101555

Errehymy, A. et al.: Physics of the Dark Universe 46(2024)101555

2024
[38]

and Gul, M.Z.: Phys

Sharif, M. and Gul, M.Z.: Phys. Scr. 99(2024)065036

2024
[39]

et al.: Chin

Gul, M.Z. et al.: Chin. J. Phys. 89(2024)1347. 26

2024
[40]

et al.: Phys

Myrzakulov, Y. et al.: Phys. Dark Universe 46(2024)101614

2024
[41]

et al.: Phys

Harko, T. et al.: Phys. Rev. D 98(2018)084043

2018
[42]

and Sahoo, P.K.: Phys

Mandal, S. and Sahoo, P.K.: Phys. Lett. B 823(2021)136786

2021
[43]

High Energy Astrophys

Myrzakulov, K.: J. High Energy Astrophys. 44(2024)164

2024
[44]

and White M.: Phys

Turner, M.S. and White M.: Phys. Rev. D 56(1997)R4439

1997
[45]

and Starobinsky, A.: Int

Sahni, V. and Starobinsky, A.: Int. J. Mod. Phys. D 15(2006)2105

2006
[46]

and Shekh, S.H.: Astron

Chirde, V.R. and Shekh, S.H.: Astron. Astrophys. 58(2015)106

2015
[47]

et al.: Phys

Arora, S. et al.: Phys. Dark Universe. 30(2020)100664

2020
[48]

et al.: Phys

Solanki, R. et al.: Phys. Dark Universe. 36(2022)100996

2022
[49]

et al.: Phys

Mussatayeva, A. et al.: Phys. Dark Universe. 42(2023)101276

2023
[50]

and Sheykhi, A.: Phys

Ebrahimi, E. and Sheykhi, A.: Phys. Lett. B 706(2011)19

2011
[51]

et al.: Int

Saaidi, K. et al.: Int. J. Mod. Phys. D 21(2012)1250057

2012
[52]

Space Sci

Jawad, A.: Astrophys. Space Sci. 356(2015)119

2015
[53]

et al.: Eur

Fayaz, V. et al.: Eur. Phys. J. Plus 131(2016)22

2016
[54]

and Nawazish, I.: Int

Sharif, M. and Nawazish, I.: Int. J. Mod. Phys. D 27(2018)1850091

2018
[55]

et al.: J

Saridakis, E.N. et al.: J. Cosmol. Astropart. Phys. 2018(2018)012

2018
[56]

and Bamba, K.: Eur

Zadeh, M.A., Sheykhi, A., Moradpour, H. and Bamba, K.: Eur. Phy s. J. C 78(2018)11

2018
[57]

et al.: Eur

Ghaﬀari, S. et al.: Eur. Phys. J. C 78(2018)706

2018
[58]

et al.: Class

Huang, Q. et al.: Class. Quantum Grav. 36(2019)175001

2019
[59]

and Banerjee, S.: Nucl

Odintsov, S.D., Oikonomou, V.K. and Banerjee, S.: Nucl. Phys. B 938(2019)935

2019
[60]

et al.: Front

Myrzakulov, N. et al.: Front. Astron. Space Sci. 9(2022)902552. 27

2022
[61]

and Hashim, I.: Phys

Sharif, M., Gul, M.Z. and Hashim, I.: Phys. Dark Universe 46(2024)101606

2024
[62]

and Hashim, I.: Chin

Sharif, M., Gul, M.Z. and Hashim, I.: Chin. J. Phys. 89(2024)266

2024
[63]

and Hashim, I.: Phys

Gul, M.Z., Sharif, M. and Hashim, I.: Phys. Dark Universe 45(2024)101537

2024
[64]

and Sahoo, P.K.: Physics 4(2022)1403

Gadbail, G.N., Mandal, S. and Sahoo, P.K.: Physics 4(2022)1403

2022
[65]

and Linder, E.V.: Phys

Caldwell, R.R. and Linder, E.V.: Phys. Rev. Lett. 95(2005)141301

2005
[66]

et al.: J

Sahni, V. et al.: J. Exp. Theor. Phys. Lett. 77(2003)201

2003
[67]

Myrzakulov, N.: Front. Astron. Space Sci. 9(2022)902552

2022
[68]

et al.: Astron

Ade, P.A. et al.: Astron. Astrophys. 594(2016)13

2016
[69]

and Ajmal, M.: Chin

Sharif, M. and Ajmal, M.: Chin. J. Phys. 88(2024)706

2024
[70]

and Ibrar, I.: Eur

Sharif, M. and Ibrar, I.: Eur. Phys. J. Plus 139(2024)17

2024
[71]

and Zubair, M.: Astrophys

Sharif, M. and Zubair, M.: Astrophys. Space Sci. 353(2014)699. 28

2014

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [1]

et al.: Astrophys

Swaters, R.A. et al.: Astrophys. J. 531(2000)107

work page 2000

[2] [2]

and Starobinsky, A.A.: Int

Sahni, V. and Starobinsky, A.A.: Int. J. Mod. Phys. D 9(2000)373; Carroll, S.M.: Living Rev. Rel. 4(2001)1

work page 2000

[3] [3]

and Odintsov, S.D.: Int

Nojiri, S.I. and Odintsov, S.D.: Int. J. Geom. Methods Mod. Phys. 4(2007)115

work page 2007

[4] [4]

and Zhitnitsky, A.R.: Phys

Urban, F.R. and Zhitnitsky, A.R.: Phys. Rev. D 80(2009)063001

work page 2009

[5] [5]

Ohta, N.: Phys. Lett. B 695(2011)41

work page 2011

[6] [6]

et al.: Phys

Cai, R.G. et al.: Phys. Rev. D 84(2011)123501

work page 2011

[7] [7]

and Movahed, M.S.: Gen

Sheykhi, A. and Movahed, M.S.: Gen. Relativ. Gravit. 44(2012)449

work page 2012

[8] [8]

et al.: Mod

Feng, C.J. et al.: Mod. Phys. Lett. A 27(2012)1250182

work page 2012