Pith. sign in

REVIEW 2 major objections 4 minor 125 references

Bulk viscous matter in $f(T)$ gravity: A path to cosmic acceleration

T0 review · 2 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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

Pith's one-line read Bulk viscous matter in $f(T)=\alpha T$ gravity, with viscosity $\zeta(t)=\zeta_0+\zeta_1 H$, fits combined cosmological data and can drive the observed transition to accelerated expansion without a dark-energy component.

desk verdict The Case I results rest on an H(z) that does not solve the paper's own Eq. (23), so the advertised path to cosmic acceleration is unsupported. read the letter →

arxiv 2501.03388 v1 pith:Z53PPSPL submitted 2025-01-06 astro-ph.CO gr-qc

Kairat Myrzakulov , O. Donmez , M. Koussour , S. Muminov , E. Davletov , J. Rayimbaev This is my paper · ORCID
classification astro-ph.COgr-qc MSC 83F0583D05 PACS 98.80.-k04.50.Kd
keywords bulkviscosityf(T)teleparallelgravitycosmicaccelerationdecelerationparameterstatefinderdiagnosticOm(z)Hubbleconstraintsquintessence
topics Dark Energy
open problems Dark Energy
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper sets out to show that the universe's late-time acceleration can be produced by bulk viscosity in the matter fluid, within teleparallel modified gravity with $f(T)=\alpha T$. It takes the viscosity coefficient to be $\zeta(t)=\zeta_0+\zeta_1 H$, derives an explicit Hubble parameter $H(z)$ from the modified Friedmann equations, and fits that expression to the combined $H(z)+\text{Pantheon}^{+}+\text{BAO}$ dataset. With the best-fit parameters the deceleration parameter changes from positive to negative, so the expansion switches from decelerating to accelerating around redshift $z\approx0.8$--$0.9$. The present-day values are $q_0\approx-0.49$ (for $\zeta_1\neq0$) and $q_0\approx-0.32$ (for $\zeta_1=0$), which the paper reads as evidence that a bulk-viscous matter component in $f(T)$ gravity can replace dark energy.

What carries the argument

The object carrying the argument is the explicit Hubble parameter $H(z)$ obtained by integrating the modified Friedmann equation under the linear torsion model $f(T)=\alpha T$ and the bulk-viscosity prescription $p_{\mathrm{eff}}=p-3\zeta(t)H$. That single function enters every subsequent diagnostic: the deceleration parameter $q$, jerk $j$, effective equation of state $\omega_{\mathrm{eff}}$, statefinder pair $(r,s)$, and $Om(z)$ are all computed from $H(z)$ or its derivatives, so the fit quality and the predicted cosmic acceleration depend entirely on this expression and on the two fitted viscosity parameters $\zeta_0$ and $\zeta_1$.

What would settle it

Direct substitution of Eq. (24) into Eq. (23) fails for $\zeta_1\neq0$: the homogeneous term needs the exponent $3(\alpha-\zeta_1)/(2\alpha)$, not $3/2$. Re-running the MCMC with the correctly integrated $H(z)$ would settle whether the quoted Case I best-fit parameters and $q_0\approx-0.49$ survive.

Watch

Extended reading notes

Core claim

The central claim is that a pressureless matter fluid with bulk viscosity $\zeta(t)=\zeta_0+\zeta_1 H$, coupled through $f(T)=\alpha T$ teleparallel gravity, yields the Hubble-rate solution $H(z)=H_0(1+z)^{3/2}+\frac{\zeta_0}{\alpha-\zeta_1}\left[1-(1+z)^{\frac{3(\alpha-\zeta_1)}{2\alpha}}\right]$, and that this solution, when fitted to $H(z)+\text{Pantheon}^{+}+\text{BAO}$ data, gives an accelerating universe without dark energy. For $\zeta_1\neq0$ the best fit is $H_0=60.0^{+2.0}_{-1.9}$ km/s/Mpc, $\alpha=1.01^{+0.10}_{-0.098}$, $\zeta_0=40.1^{+1.9}_{-2.0}$, and $\zeta_1=0.123^{+0.093}_{-0.088}$; for $\zeta_1=0$ it is $H_0=67.5^{+1.3}_{-1.3}$ km/s/Mpc, $\alpha=0.94^{+0.14}_{-0.13}$, and $\zeta_0=34.7^{+2.0}_{-2.0}$. The resulting jerk parameter, effective equation of state, statefinder trajectories, and $Om(z)$ diagnostic all indicate quintessence-like behavior, with the model approaching the $\Lambda$CDM fixed point in the far future.

Load-bearing premise

The load-bearing premise is that the Hubble parameter expression in Eq. (24) is the correct integral of Eq. (23) when $\zeta_1\neq0$; if that integration is not correct, every Case I parameter constraint and diagnostic built on it has to be recomputed.

Editorial extensions

If this is right

  • If the model is correct, no cosmological constant or scalar field is needed: the negative effective pressure that accelerates the expansion comes from the bulk-viscosity term $-3\zeta H$ in a universe dominated by ordinary matter.
  • The combined dataset fixes the parameters tightly enough to predict a transition redshift $z_{\mathrm{tr}}\approx0.90$ for $\zeta_1\neq0$ and $z_{\mathrm{tr}}\approx0.80$ for $\zeta_1=0$, with present-day deceleration $q_0\approx-0.49$ and $-0.32$.
  • The statefinder and $Om(z)$ trajectories lie in the quintessence region and converge to the $\Lambda$CDM fixed point $(r,s)=(1,0)$ and the de Sitter point $(r,q)=(1,-1)$ in the future, so the model mimics $\Lambda$CDM at late times while differing at intermediate redshifts.
  • The fitted $\alpha$ values are close to $1$, so the model can be viewed as a small torsion-gravity correction to the standard Friedmann dynamics of a viscous fluid.

Reading between the lines

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

  • The same derivation could be repeated for nonlinear $f(T)$ models, such as adding a quadratic torsion term, where the torsion correction and the viscous pressure would interact; those extended models could be tested against the same $H(z)$, Pantheon+, and BAO data.
  • The gap between the inferred $H_0$ values in the two cases ($\approx60$ versus $\approx67.5$ km/s/Mpc) suggests that deciding whether viscosity scales with $H$ strongly affects the Hubble-constant estimate; a formal model-selection comparison between the two cases is a natural next step.
  • Because every quoted diagnostic is a functional of the single $H(z)$ expression, a reader can reconstruct the entire analysis from Eqs. (20)--(24) and the quoted best-fit parameters; no additional closure assumptions are needed to reproduce the figures.
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

2 major / 4 minor

Summary. The manuscript considers a flat FLRW universe in f(T)=αT teleparallel gravity whose matter content is a pressureless fluid with bulk viscosity ζ(t)=ζ0+ζ1H. It solves the background Friedmann equation for two cases (ζ1≠0 and ζ1=0), fits the resulting H(z) to the combined H(z)+Pantheon++BAO dataset with an MCMC, and studies the deceleration, jerk, effective EoS, statefinder, and Om(z) diagnostics. The abstract reports accelerating solutions with q0≈−0.49 (Case I) and q0≈−0.32 (Case II) and concludes that bulk viscous matter in f(T) gravity can explain cosmic acceleration without dark energy.

Significance. The idea is not without interest: a single viscous matter component in a simple f(T) gravity could in principle mimic dark energy, and the paper uses standard cosmological datasets with a clearly stated likelihood. The analytical derivation is also checkable, which is a strength. However, the main announced result (Case I) is built on an incorrect solution of the model's own field equation, so none of the Case I constraints or diagnostics can be trusted. In addition, the paper's diagnostics are deterministic functions of the fitted parameters and are not independent tests. As it stands, the manuscript does not provide credible evidence for the claimed path to cosmic acceleration.

major comments (2)
  1. [III, Eqs. (23)–(24)] Equation (24) is not the solution of Eq. (23) for ζ1≠0. Writing Eq. (23) as dH/d ln a + A H = B with A=3(α−ζ1)/(2α) and B=3ζ0/(2α), the general solution is H(z)=H0(1+z)^A + (B/A)[1−(1+z)^A] = H0(1+z)^{3(α−ζ1)/(2α)} + ζ0/(α−ζ1)[1−(1+z)^{3(α−ζ1)/(2α)}]. Equation (24) instead uses H0(1+z)^{3/2} for the homogeneous term, so direct substitution leaves a residual (A−3/2)H0(1+z)^{3/2}. Since ζ1≠0, A≠3/2 and Eq. (24) does not satisfy Eq. (23). Every Case I result—the best-fit parameters in Fig. 1, H(z) in Fig. 3, q0≈−0.49, j0≈0.68, and the statefinder and Om(z) curves—is computed from this invalid expression and must be either recomputed with the correct solution or removed.
  2. [V–VII] The claimed confirmation of acceleration is partly circular. The deceleration, jerk, EoS, statefinder, and Om(z) are evaluated by inserting the best-fit parameters from Section IV into the same H(z) that was fitted to the data; they are not independent predictions. To substantiate the title's claim, the paper needs at least a model comparison (for example Δχ², AIC, or DIC relative to ΛCDM and to Case II) and a demonstration that the fitted model is statistically preferred. Without this, the statement that the model explains acceleration is largely a restatement of the fit.
minor comments (4)
  1. [IV] The MCMC description should report the burn-in length, convergence diagnostics (such as Gelman-Rubin statistics), and the final χ² per degree of freedom; otherwise the quoted 1σ intervals cannot be independently checked.
  2. [V.C and Conclusion] The text says 'the present-day values of the jerk parameter are approximately ω0≈−0.78 and ω0≈−0.55', but ω0 is the effective EoS parameter, not the jerk parameter; this sentence should be corrected.
  3. [III and IV] The units of ζ0 and ζ1 should be reconciled with the use of H in km/s/Mpc; as written, ζ=ζ0+ζ1H mixes quantities whose physical dimensions differ unless H is converted to s⁻¹ or natural units are explicitly specified.
  4. [Figures 4–11] The diagnostic curves are shown only for best-fit parameter values; including MCMC uncertainty bands would make the plots more informative and would also clarify how robust the quoted q0, j0, and ωeff values are.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: diagnostics are derived from best-fit parameters, not independent predictions; the main defect is an algebraic inconsistency rather than a circular argument.

full rationale

The paper fits (H0, alpha, zeta0, zeta1) to the combined H(z)+Pantheon+BAO data and then computes q, j, omega_eff, statefinder, and Om(z) from the resulting H(z). These quantities are deterministic functions of the fitted parameters, so they are not out-of-sample predictions; however, the paper does not present them as independent confirmations. The abstract and conclusion describe them as 'the analysis reveals' and 'determined,' not as predictions from first principles. No self-citation is load-bearing: the several works by the same group are cited only as comparisons for q0, j0, and omega0 values, not to justify the model's uniqueness or validity. The serious problem in the paper is mathematical, not circular: Eq. (24) does not follow from integrating Eq. (23) when zeta1 != 0, because the first term should have exponent 3(alpha-zeta1)/(2 alpha), not 3/2. That invalidates the Case I fits and all Case I diagnostics, but an incorrect solution is not a reduction of the conclusion to its inputs. Since circularity requires exhibiting Eq. X = Eq. Y by construction or a fitted parameter renamed as a prediction, and neither is present, the circularity score is 0.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claim rests on four fitted parameters (H0, alpha, zeta0, zeta1) and on several modeling assumptions: flat FLRW, linear f(T), the bulk viscosity ansatz, pressureless matter, and a unit choice for kappa^2. No new entities are introduced.

free parameters (4)
  • H0 = 60.0^{+2.0}_{-1.9} (Case I), 67.5^{+1.3}_{-1.3} (Case II) km/s/Mpc
    Present-day Hubble constant; fitted to H(z)+Pantheon+BAO data.
  • alpha = 1.01^{+0.10}_{-0.098} (Case I), 0.94^{+0.14}_{-0.13} (Case II)
    Linear f(T) coefficient; fitted to combined data.
  • zeta0 = 40.1^{+1.9}_{-2.0} (Case I), 34.7^{+2.0}_{-2.0} (Case II) kg/m/s
    Constant bulk viscosity term; fitted.
  • zeta1 = 0.123^{+0.093}_{-0.088} (only Case I)
    Hubble-proportional viscosity coefficient; fitted in Case I only.
assumptions (5)
  • domain assumption Flat FLRW metric (ds2 = -dt2 + a2(dx2+dy2+dz2))
    Standard cosmological assumption; used throughout Sec. III.
  • domain assumption f(T) = alpha T with alpha not equal to 0
    Simplest linear form of teleparallel gravity; Eq. (19).
  • ad hoc to paper Bulk viscosity coefficient zeta(t)=zeta0+zeta1 H
    Phenomenological ansatz introduced in Eq. (16) without microphysical derivation; the negative pressure it produces is what drives acceleration.
  • domain assumption Pressureless dust (p=0) for matter
    Assumed in Sec. III to set p=0 in effective pressure.
  • domain assumption kappa^2 = 1
    Unit choice for gravitational coupling; simplifies Friedmann equations (20)-(21).

how reviews work

0 comments
Cite this review

Pith. "Pith review of Bulk viscous matter in $f(T)$ gravity: A path to cosmic acceleration." pith.science (2026). https://pith.science/paper/Z53PPSPL

@misc{pith2026250103388,
  author       = {Pith},
  title        = {Pith review of: Bulk viscous matter in $f(T)$ gravity: A path to cosmic acceleration},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Z53PPSPL}},
  note         = {Machine review of arXiv:2501.03388}
}
abstract

In this paper, we investigate the effects of varying bulk viscosity coefficients $\zeta(t)=\zeta_{0}+\zeta_{1}H$ on cosmic evolution within the framework of $f(T)$ teleparallel gravity. We focus on two cases: (i) $\zeta_{1} \neq0$ and (ii) $\zeta_{1} =0$, deriving the Hubble parameter $H$ as a function of redshift $z$ using a linear $f(T)$ model ($f(T) = \alpha T$ where $\alpha \neq 0$). Using the combined $H(z)+Pantheon^{+}+BAO$ dataset, we obtain observational constraints on model parameters. For Case I ($\zeta_1 \neq 0$), best-fit values are $H_0=60.0^{+2.0}_{-1.9}$ km/s/Mpc, $\alpha=1.01^{+0.10}_{-0.098}$, $\zeta_0=40.1^{+1.9}_{-2.0}$, and $\zeta_1=0.123^{+0.093}_{-0.088}$, while for Case II ($\zeta_1 = 0$), they are $H_0=67.5^{+1.3}_{-1.3}$ km/s/Mpc, $\alpha=0.94^{+0.14}_{-0.13}$, and $\zeta_0=34.7^{+2.0}_{-2.0}$. The analysis reveals a transition in the deceleration parameter, indicating a shift from deceleration to acceleration of the universe's expansion, with present-day values of $q_{0} \approx -0.49$ and $q_{0} \approx -0.32$ for the respective cases. The jerk parameter $j(z)$ and effective EoS for the cosmic viscous fluid also support the cosmic acceleration, with trajectories aligning with the quintessence scenario. These findings underscore the potential of our $f(T)$ model dominated by bulk viscous matter in explaining cosmic acceleration.

Figures

Figures reproduced from arXiv: 2501.03388 by the authors.

Figure 1
Figure 1. FIG. 1: The constrained values for the model parameters [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: The constrained values for the model parameters [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: The behavior of the Hubble parameter [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (4 more)
Figure 6
Figure 6. Figure 6: FIG. 6: The behavior of the energy density [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: The behavior of the effective pressure [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 9
Figure 9. Figure 9: FIG. 9: The behavior of the [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10: The behavior of the [PITH_FULL_IMAGE:figures/full_fig_p010_10.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

125 extracted references · 66 canonical work pages

  1. [1]

    Einstein, Sitzungsberichte der K¨oniglich Preussischen Akademie der Wissenschaften zu Berlin, 831 (1995)

    A. Einstein, Sitzungsberichte der K¨oniglich Preussischen Akademie der Wissenschaften zu Berlin, 831 (1995)

    1995

  2. [2]

    Hilbert, Nachrichten von der Gesellschaft der Wis- senschaften zu G ¨ottingen - Mathematisch - Physikalis- cheKlasse, 3, 395 (1915)

    D. Hilbert, Nachrichten von der Gesellschaft der Wis- senschaften zu G ¨ottingen - Mathematisch - Physikalis- cheKlasse, 3, 395 (1915)

    1915

  3. [3]

    Further, the present-day values of the jerk parameter are approximately ω0 ≈ −0.78 and ω0 ≈ −0.55 for the respective cases [115–118]

    in the present epoch and converges to the EoS of ΛCDM ( ωΛ = −1) in the distant future. Further, the present-day values of the jerk parameter are approximately ω0 ≈ −0.78 and ω0 ≈ −0.55 for the respective cases [115–118]. The same figure shows the evolution of ωe f f for different cases of the bulk viscos- ity parameter ζ0. Specifically, we observe a sign...

  4. [4]

    Einstein, Ann

    A. Einstein, Ann. Phys., 354, 769 (1916)

    1916

  5. [5]

    Landau and E.M

    L.D. Landau and E.M. Lifshitz, The Classical Theory of Fields (Pergamon Press, Oxford 1970)

    1970

  6. [6]

    Shapiro, W.B

    I.I. Shapiro, W.B. Smith, M.E. Ash, and S. Herrick, As- tron. J., 76, 588 (1971)

    1971

  7. [7]

    Shapiro, C.C

    I.I. Shapiro, C.C. Counselman, R.W. King, Phys. Rev. Lett., 36, 555 (1976)

    1976

  8. [8]

    Taylor and J.M

    J.H. Taylor and J.M. Weisberg, Astrophys. J., 253, 908 (1982)

    1982

Show all 125 references
  1. [9]

    Will, Living Rev

    C.M. Will, Living Rev. Relat., 17, 4 (2014)

    2014

  2. [10]

    Ishak, Living Rev

    M. Ishak, Living Rev. Relat., 22, 1 (2019)

    2019

  3. [11]

    Abbott et al., Phys

    B.P . Abbott et al., Phys. Rev. Lett.,116, 061102 (2016)

    2016

  4. [12]

    Riess et al., Astrophys

    A.G. Riess et al., Astrophys. J., 116, 1009 (1998)

    1998

  5. [13]

    Perlmutter et al., Astrophys

    S. Perlmutter et al., Astrophys. J., 517, 377 (1999)

    1999

  6. [14]

    Eisenstein et al., Astrophys

    D.J. Eisenstein et al., Astrophys. J., 633, 560 (2005)

    2005

  7. [15]

    Percival et al., S, Mon

    W.J. Percival et al., S, Mon. Not. Roy. Astron. Soc., 381 1053 (2007)

    2007

  8. [16]

    Komatsu et al., Astrophys

    E. Komatsu et al., Astrophys. J., 192, 18 (2011)

    2011

  9. [17]

    Buchdahl, Month

    H.A. Buchdahl, Month. Not. R. Astron. Soc., 150, 1 (1970)

    1970

  10. [18]

    Barrow and A.C

    J.D. Barrow and A.C. Ottewill, J. Phys. A: Math. Gen.,16, 2757 (1983)

    1983

  11. [19]

    A. A. Starobinsky, JETP Letters, 86, 157 (2007)

    2007

  12. [20]

    Capozziello, V

    S. Capozziello, V . F. Cardone, V . Salzano, Phys. Rev. D, 78, 063504 (2008)

    2008

  13. [21]

    Chiba, T.L

    T. Chiba, T.L. Smith, A.L. Erickcek, Phys. Rev. D, 75, 124014 (2007)

    2007

  14. [22]

    Astorga-Moreno and E.A

    J.A. Astorga-Moreno and E.A. Mena-Barboza, Phys. Lett. A, 481, 129012 (2023)

    2023

  15. [23]

    Harko et al., Phys

    T. Harko et al., Phys. Rev. D, 84, 024020 (2011)

    2011

  16. [24]

    Moraes, P .K

    P .H.R.S. Moraes, P .K. Sahoo, Phys. Rev. D, 96, 044038 (2017)

    2017

  17. [25]

    Amani and A

    A.R. Amani and A. Samiee-Nouri, Commun. Theor. Phys., 64, 485 (2015)

    2015

  18. [26]

    J. B. Jimenez et al., Phys. Rev. D, 98, 044048 (2018). 12

    2018

  19. [27]

    De Laurentis, M

    M. De Laurentis, M. Paolella, S. Capozziello, Phys. Rev. D, 91, 083531 (2015)

    2015

  20. [28]

    de la Cruz-Dombriz, D

    A. de la Cruz-Dombriz, D. S-Gomez, Class. Quantum Grav., 29, 245014 (2012)

    2012

  21. [29]

    Weitzenb ¨ock, Invariantentheorie (Noordhoff, Gronin- gen, 1923)

    R. Weitzenb ¨ock, Invariantentheorie (Noordhoff, Gronin- gen, 1923)

    1923

  22. [30]

    Einstein, Preussische Akademie der Wissenschaften, Phys

    A. Einstein, Preussische Akademie der Wissenschaften, Phys. math. Klasse, Sitzungsberichte, 1928, 217 (1928)

    1928

  23. [31]

    M ¨oller, Mat

    C. M ¨oller, Mat. Fys. Skr. Dan. Vid. Selsk.,1, 10 (1961)

    1961

  24. [32]

    Pellegrini and J

    C. Pellegrini and J. Plebanski, Mat. Fys. Skr. Dan. Vid. Selsk., 2, 4 (1963)

    1963

  25. [33]

    Hayashi and T

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

    1979

  26. [34]

    Aldrovandi and J.G

    R. Aldrovandi and J.G. Pereira, Teleparallel Gravity, vol. 173 (Fundamental Theories of Physics (Springer, Heidel- berg, 2013)

    2013

  27. [35]

    Paliathanasis, J

    A. Paliathanasis, J. D. Barrow, P . G. L. Leach, Phys. Rev. D, 94, 023525 (2016)

    2016

  28. [36]

    I. G. Salako et al., J. Cosmol. Astropart. Phys., 11 060 (2013)

    2013

  29. [37]

    Myrzakulov, Eur

    R. Myrzakulov, Eur. Phys. J. C, 71, 1752 (2011)

    2011

  30. [38]

    Bamba et al., J

    K. Bamba et al., J. Cosmol. Astropart. Phys., 01, 021 (2011)

    2011

  31. [39]

    S-Hung Chen et al., Phys. Rev. D, 83, 023508 (2011)

    2011

  32. [40]

    B. Li, T.P . Sotiriou, and J.D. Barrow, Phys. Rev. D, 83, 104017 (2011)

    2011

  33. [41]

    Capozziello et al., Phys

    S. Capozziello et al., Phys. Rev. D, 84, 043527 (2011)

    2011

  34. [42]

    Liu and M.J

    D. Liu and M.J. Reboucas, Phys. Rev. D, 86, 083515 (2012)

    2012

  35. [43]

    Cai et al., Class

    Y.F. Cai et al., Class. Quantum Gravity,28, 215011 (2011)

    2011

  36. [44]

    Jamil, D

    M. Jamil, D. Momeni, and R. Myrzakulov, Eur. Phys. J. C, 73, 1-13 (2013)

    2013

  37. [45]

    Rodrigues et al., Phys

    M.E. Rodrigues et al., Phys. Rev. D, 86, 104059 (2012)

    2012

  38. [46]

    Koussour and M

    M. Koussour and M. Bennai, Class. Quantum Gravity, 39, 105001 (2022)

    2022

  39. [47]

    Nunes, S

    R.C. Nunes, S. Pan, and E.N. Saridakis, J. Cosmol. As- tropart. Phys., 08, 011 (2016)

    2016

  40. [48]

    Yang, R.H

    J. Yang, R.H. Lin, and X.H. Zhai, Eur. Phys. J. C, 82, 1-11 (2022)

    2022

  41. [49]

    Ganjizadeh, A

    S. Ganjizadeh, A. Amani, and M.A. Ramzanpour, Chin. Phys. C, 46, 125104 (2022)

    2022

  42. [50]

    Rezaei and A

    T.M. Rezaei and A. Amani, Can. J. Phys., 95, 1068-1073 (2017)

    2017

  43. [51]

    Misner, Astrophys

    W. Misner, Astrophys. J., 151, 431 (1968)

    1968

  44. [52]

    Israel and J.N

    W. Israel and J.N. Vardalas, Nuovo Cimento Lett., 4, 887 (1970)

    1970

  45. [53]

    Murphy, Phys

    G.L. Murphy, Phys. Rev. D, 8, 4231 (1973)

    1973

  46. [54]

    Belinskii and I.M

    V .A. Belinskii and I.M. Kalatnikov, Pisma Zh. Eksp. Tekhn. Fiz., 21, 223 (1974)

    1974

  47. [55]

    Diosi, B

    L. Diosi, B. Keszthelyi, B. Lukacs, and G. Paal, Acta Phys. Pol. B, 15, 909 (1984)

    1984

  48. [56]

    Waga, R.C

    I. Waga, R.C. Falcao, and R. Chanda, Phys. Rev. D, 33, 1839 (1986)

    1986

  49. [57]

    Barrow, Phys

    J.D. Barrow, Phys. Lett., 180, 335 (1986)

    1986

  50. [58]

    Barrow, Nucl

    J.D. Barrow, Nucl. Phys. B, 380, 743 (1988)

    1988

  51. [59]

    Zimdahl, D.J

    W. Zimdahl, D.J. Schwarz, A.B. Balakin, and D. Pavon, Phys. Rev. D, 64, 063501 (2001)

    2001

  52. [60]

    Velten and D.J

    H. Velten and D.J. Schwarz, Phys. Rev. D, 86, 083501 (2012)

    2012

  53. [61]

    Setare and A

    M.R. Setare and A. Sheykhi, Int. J. Mod. Phys. D,19, 1205 (2010)

    2010

  54. [62]

    Cataldo, N

    M. Cataldo, N. Cruz, and S. Lepe, Phys. Lett. B, 619, 5 (2005)

    2005

  55. [63]

    Brevik and O

    I. Brevik and O. Gorbunova, Gen. Relativ. Gravit., 37, 2039 (2005)

    2005

  56. [64]

    Cos- mol

    Jean-Sebastien Gagnon and Julien Lesgourgues, J. Cos- mol. Astropart. Phys., 09, 026 (2011)

    2011

  57. [65]

    Brevik, E

    I. Brevik, E. Elizalde, and S.D. Odintsov, Phys. Rev. D, 84, 103508 (2001)

    2001

  58. [66]

    Gron, Astrophys.Space Sci., 173, 191-225 (1990)

    O. Gron, Astrophys.Space Sci., 173, 191-225 (1990)

    1990

  59. [67]

    Eckart, Phys

    C. Eckart, Phys. Rev.,, 58, 919 (1940)

    1940

  60. [68]

    Li and J.D

    B. Li and J.D. Barrow, Phys. Rev. D, 79, 103521 (2009)

    2009

  61. [69]

    Hipolito-Ricaldi, H.E.S

    W.S. Hipolito-Ricaldi, H.E.S. Velten, and W. Zimdahl, J. Cosmol. Astropart. Phys., 06, 016 (2009)

    2009

  62. [70]

    Montiel and N

    A. Montiel and N. Bretn, J. Cosmol. Astropart. Phys., 08, 023 (2011)

    2011

  63. [71]

    Hu and X.-H

    M.G. Hu and X.-H. Meng, Phys. Lett. B, 635, 186 (2006)

    2006

  64. [72]

    Jie Ren and Xin-He Meng, Phys. Lett. B, 633, 1 (2006)

    2006

  65. [73]

    Gagnon and J

    J.S. Gagnon and J. Lesgourgues, J. Cosmol. Astropart. Phys., 09, 026 (2011)

    2011

  66. [74]

    Ryden, Introduction to Cosmology (Addison Wesley, San Francisco, United States of America, 2003)

    B. Ryden, Introduction to Cosmology (Addison Wesley, San Francisco, United States of America, 2003)

    2003

  67. [75]

    Meng and X

    X.H. Meng and X. Dou, Commun. Theor. Phys., 52, 377 (2009)

    2009

  68. [76]

    X.H. Meng, J. Ren, and M.G. Hu, Commun. Theor. Phys., 47, 379 (2007)

    2007

  69. [77]

    Avelino, U

    A. Avelino, U. Nucamendi, J. Cosmol. Astropart. Phys., 9, 1008 (2010)

    2010

  70. [78]

    Sharif and S

    M. Sharif and S. Rani , Mod. Phys. Lett. A, 28, 1350118 (2013)

    2013

  71. [79]

    D. F. Mackey et al., Publ. Astron. Soc. Pac., 125, 306 (2013)

    2013

  72. [80]

    Jimenez et al., Astrophys

    R. Jimenez et al., Astrophys. J. 593, 622 (2003)

    2003

  73. [81]

    Simon, L

    J. Simon, L. Verde, and R. Jimenez, Phys. Rev. D 71, 123001 (2005)

    2005

  74. [82]

    Stren et al., J

    D. Stren et al., J. Cosmol. Astropart. Phys. 2010, 008 (2010)

    2010

  75. [83]

    Moresco et al., J

    M. Moresco et al., J. Cosmol. Astropart. Phys. 2012, 006 (2010)

    2010

  76. [84]

    Zhang et al., Res

    C. Zhang et al., Res. Astron. Astrophys. 14, 1221 (2014)

    2014

  77. [85]

    Moresco, Mon

    M. Moresco, Mon. Not. Roy. Astron. Soc. 450, L16 (2015)

    2015

  78. [86]

    Moresco et al., J

    M. Moresco et al., J. Cosmol. Astropart. Phys. 2016, 014 (2016)

    2016

  79. [87]

    Jimenez and A

    R. Jimenez and A. Loeb, Astrophys. J. 573, 37 (2002)

    2002

  80. [88]

    Scolnic et al., Astrophys

    D. Scolnic et al., Astrophys. J., 938, 113 (2022)

    2022

  81. [89]

    Brout et al., Astrophys

    D. Brout et al., Astrophys. J., 938, 110 (2022)

    2022

  82. [90]

    Blake et al., Mon

    C. Blake et al., Mon. Not. Roy. Astron. Soc. , 418, 1707 (2011)

    2011

  83. [91]

    W. J. Percival et al., Mon. Not. Roy. Astron. Soc. , 401, 2148 (2010)

    2010

  84. [92]

    Beutler et al., Mon

    F. Beutler et al., Mon. Not. Roy. Astron. Soc. , 416, 3017 (2011)

    2011

  85. [93]

    Jarosik et al., Astrophys

    N. Jarosik et al., Astrophys. J. Suppl., 192, 14 (2011)

    2011

  86. [94]

    D. J. Eisenstein et al., Astrophys. J., 633, 560 (2005)

    2005

  87. [95]

    Giostri et al., J

    R. Giostri et al., J. Cosm. Astropart. Phys., 1203, 027 (2012)

    2012

  88. [96]

    Aghanim et al., Astron

    N. Aghanim et al., Astron. Astrophys., 641, A6 (2020). 13

    2020

  89. [97]

    Cunha and J.A.S

    J.V . Cunha and J.A.S. Lima, Mon. Not. Roy. Astron. Soc. , 390, 210 (2008)

    2008

  90. [98]

    Cunha,Phys

    J.V . Cunha,Phys. Rev. D, 79, 047301 (2009)

    2009

  91. [99]

    Nair et al., J

    R. Nair et al., J. Cosmol. Astropart. Phys. , 01, 018 (2012)

    2012

  92. [100]

    Koussour et al., Results Phys., 55, 107166 (2023)

    M. Koussour et al., Results Phys., 55, 107166 (2023)

    2023

  93. [101]

    Wang et al., Eur

    D. Wang et al., Eur. Phys. J. C, 83, 1-14 (2023)

    2023

  94. [102]

    Koussour et al., Eur

    M. Koussour et al., Eur. Phys. J. Plus, 139, 1-13 (2023)

    2023

  95. [103]

    Koussour et al., Chin

    M. Koussour et al., Chin. J. Phys. 90, 108-120 (2024)

    2024

  96. [104]

    Myrzakulov et al

    Y. Myrzakulov et al. arXiv, arXiv:2407.08837 (2024)

    2024 arXiv

  97. [105]

    Myrzakulov et al., Phys

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

    2024

  98. [106]

    Myrzakulov et al., J

    K. Myrzakulov et al., J. High Energy Astro. Phys. 44, 164- 171 (2024)

    2024

  99. [107]

    Zhadyranova et al., J

    A. Zhadyranova et al., J. High Energy Astro. Phys. 44, 123- 131 (2024)

    2024

  100. [108]

    Koussour et al., Chin

    M. Koussour et al., Chin. J. Phys. 91, 445-457 (2024)

    2024

  101. [109]

    Myrzakulov et al., J

    Y. Myrzakulov et al., J. High Energy Astro. Phys. 43, 209- 216 (2024)

    2024

  102. [110]

    Myrzakulov et al., Eur

    Y. Myrzakulov et al., Eur. Phys. J. C 87, 665 (2024)

    2024

  103. [111]

    Visser, Class

    M. Visser, Class. Quantum Gravity, 21, 2603 (2004)

    2004

  104. [112]

    Visser, Gen

    M. Visser, Gen. Relativ. Gravit., 37, 1541-1548 (2005)

    2005

  105. [113]

    Myrzakulov, M

    N. Myrzakulov, M. Koussour and D.J. Gogoi, Eur. Phys. J. C, 83, 594 (2023)

    2023

  106. [114]

    Tsujikawa, Class

    S. Tsujikawa, Class. Quant. Grav., 30, 214003 (2013)

    2013

  107. [115]

    R. R. Caldwell, Phys. Lett. B, 545, 23 (2002)

    2002

  108. [116]

    Koussour and A

    M. Koussour and A. De, Eur. Phys. J. C, 83, 400 (2023)

    2023

  109. [117]

    Mukherjee, Mon

    A. Mukherjee, Mon. Not. R. Astron. Soc., 460, 273-282 (2016)

    2016

  110. [118]

    Dark Universe,34, 100889 (2021)

    A N `ajera and A Fajardo, Phys. Dark Universe,34, 100889 (2021)

    2021

  111. [119]

    Myrzakulov et al., Eur

    N. Myrzakulov et al., Eur. Phys. J. Plus, 138, 852 (2023)

    2023

  112. [120]

    Sahni et al., J

    V . Sahni et al., J. Exp. Theor. Phys. Lett., 77, 201-206 (2003)

    2003

  113. [121]

    alam et al., Mon

    U. alam et al., Mon. Not. Roy. Astron. Soc., 344, 1057 (2003)

    2003

  114. [122]

    Sahni, A

    V . Sahni, A. Shafieloo and A. A. Starobinsky, Phys. Rev. D, 78, 103502 (2008)

    2008

  115. [123]

    Singh and A

    C.P . Singh and A. Kumar, Mod. Phys. Lett. A,33, 1850225 (2018)

    2018

  116. [124]

    Singh and A

    C.P . Singh and A. Kumar, Eur. Phys. J. Plus, 133, 312 (2018)

    2018

  117. [125]

    Singh and M

    C.P . Singh and M. Srivastava, Eur. Phys. J. C, 78, 190 (2018)

    2018

Pith tools

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