Pith. sign in

REVIEW 4 major objections 4 minor 35 references

Observational constraints on holography in $(2 + 1)$-dimensional cosmology with a generalized equation of state

T0 review · 4 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

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

Pith's one-line read In (2+1)-dimensional FLRW cosmology with the generalized equation of state $p=(\zeta-1)(\rho+\rho_0)$, the Fischler–Susskind holographic bound $S/A\le1$ holds for flat and open universes, fails for closed ones, and fails for flat universes

desk verdict The paper's central claim rests on a bad algebra step (Eq. 13), and the 'observational constraints' never constrain the paper's own parameters; I'd reject it, not because the topic is uninteresting but because the support is missing. read the letter →

arxiv 2508.11701 v1 pith:O3ABIWYO submitted 2025-08-13 physics.gen-ph gr-qchep-th

Praveen Kumar Dhankar , Safiqul Islam , Saibal Ray , Aritra Sanyal , S. K. Maurya This is my paper · ORCID
classification physics.gen-phgr-qchep-th PACS 98.80.-k
keywords holographicprincipleFischler–Susskindbound(2+1)-dimensionalgravitygeneralizedequationofstatenegativecosmologicalconstantFriedmanncosmologyHubbleparameterdataMarkovchainMonteCarlo
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

The paper asks whether the Fischler–Susskind cosmic holographic bound — entropy inside a horizon must not exceed the boundary area — survives in a (2+1)-dimensional universe governed by a generalized equation of state $p=(\zeta-1)(\rho+\rho_0)$ with free parameters $\zeta$ and $\rho_0$. Working out the (2+1)-dimensional Friedmann solutions, the authors find the entropy-to-area ratio $S/A$ declines as flat ($k=0$) and open ($k=-1$) universes expand, so the bound holds there; it fails in closed ($k=+1$) universes at the turning point, and also in flat models once a negative cosmological constant ($\rho_0<0$) forces recollapse, where $S/A$ exceeds unity after maximum expansion for $1<\zeta\le2$. These are exactly the behaviors Kaloper and Linde found in four dimensions, so the upshot is that holography's geometric pattern is robust across dimensions. A Markov-chain Monte Carlo fit to 30 Hubble parameter measurements yields $H_0\simeq68.16$, $\Omega_m\simeq0.32$, consistent with Planck/$\Lambda$CDM, lending the model observational viability. If the claims hold, lower-dimensional gravity — where the field equations are exactly solvable — becomes a clean laboratory for testing entropy bounds.

What carries the argument

The generalized equation of state $p=(\zeta-1)(\rho+\rho_0)$ (dust at $\zeta=1$, radiation at $\zeta=3/2$ with $\rho_0=0$) together with the $(2+1)$-dimensional Friedmann equations $\dot a^2+k=2\pi G\rho a^2$. The holographic ratio is carried by the Wang–Abdalla entropy assignment $S=\sigma L_H$ with constant comoving entropy density $\sigma$ and particle horizon $L_H=a r_H$, giving $S/A=\sigma r_H/a$ with $A=a^2$. The decisive computation is the horizon size at the turning point of a recollapsing universe, evaluated as an Euler $\beta$ function, $L_H^{\rm turn}=(2\zeta\sqrt{\lambda})^{-1}B((\zeta-1)/2\zeta,1/2)$, which converts the bound into the scaling $S/A\sim\lambda^{1/\zeta-1/2}$.

What would settle it

Numerically integrate the exact scale factor $a(t)=[(2\beta_0 G/\lambda)^{1/2\zeta}\sin(\zeta\sqrt{\lambda}\,t)]^{1/\zeta}$ for $\zeta=3/2$ and small $\lambda$, and compute $S/A=\sigma r_H/a$ through the recollapse: the claimed violation requires the ratio to cross unity after the turning point. Then recompute the ratio using the apparent horizon as the boundary; if $S/A$ never exceeds 1 there, the breakdown is an artifact of using the particle horizon.

Watch

Extended reading notes

Core claim

For $p=(\zeta-1)(\rho+\rho_0)$ in $(2+1)$-dimensional FLRW cosmology, with entropy $S=\sigma L_H$ inside the particle horizon and boundary area $A=a^2$, the holographic ratio is $S/A=\sigma r_H/a$. In dust and flat radiation-dominated models this ratio falls as the universe expands, so the bound $S/A\le1$ holds for $k=0,-1$ once it holds initially. In a closed universe the horizon area vanishes at maximum expansion and the bound is breached at the turning point. In a flat model with negative cosmological constant ($\rho_0<0$), the scale factor behaves as $a(t)\sim[\sin(\zeta\sqrt{\lambda}\,t)]^{1/\zeta}$; the bound holds before the turning point but afterwards $S/A\sim\$$\lambda$^{{1/\zeta-1/2}}$\g

Load-bearing premise

The argument assumes, following Wang and Abdalla, that the entropy in (2+1)-dimensional cosmology is a constant comoving entropy density times the particle-horizon size, and that the holographic boundary area is just the scale factor squared; if the entropy density changes with time or the true boundary is the apparent horizon, the claimed violations after the turning point need not occur.

Editorial extensions

If this is right

  • The Fischler–Susskind bound is dimensionally robust: in $2+1$ dimensions, as in $3+1$, flat and open universes satisfy $S/A\le1$ whenever the initial entropy density obeys $\sigma\le1$.
  • A closed $(2+1)$-dimensional universe cannot satisfy the holographic bound at its turning point; preserving holography there would require exotic negative-pressure matter or a revised formulation of the bound.
  • A negative cosmological constant enforces holographic breakdown in flat $(2+1)$D models after maximum expansion, in the parameter window $1<\zeta\le2$, even while the universe is still classically large.
  • The generalized equation of state fits the 30-point Hubble dataset with $H_0\simeq68.16$ and $\Omega_m\simeq0.32$, consistent with Planck/$\Lambda$CDM, so the model is observationally viable.

Reading between the lines

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

  • Recomputing $S/A$ with the apparent horizon instead of the particle horizon is a direct test of whether the claimed violations are genuine: in a recollapsing universe the apparent horizon shrinks, and the bound may survive.
  • The same equation of state in $(3+1)$ dimensions should show the identical $\zeta<2$ violation window after maximum expansion; a quantitative side-by-side comparison would turn the paper's dimensional-robustness claim from qualitative to exact.
  • The best-fit $H_0\simeq68.16$ sits below the local distance-ladder value, so adding baryon-acoustic-oscillation or higher-redshift $H(z)$ data could shift the best-fit parameters and sharpen the model's low-redshift predictions against $\Lambda$CDM.
  • If the particle-horizon entropy bound genuinely fails for closed slicings in $2+1$ dimensions, the natural fix is a covariant entropy bound on light-sheets, which does not depend on the choice of horizon surface.
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

4 major / 4 minor

Summary. The paper studies the Fischler-Susskind holographic bound S/A ≤ 1 in (2+1)-dimensional FLRW cosmologies with a generalized linear equation of state p=(ζ−1)(ρ+ρ0). It claims that the holographic principle holds for flat (k=0) and open (k=−1) universes, fails for closed (k=+1) universes, and also fails for flat models with a negative cosmological constant. The authors then fit a ΛCDM-like H(z) expression to 30 observational Hubble data points using MCMC and conclude that the model is observationally viable. The central holography analysis is built on the entropy ansatz S=σL_H with comoving entropy density σ and area A=a^2, following Wang and Abdalla.

Significance. If the claims were correct, the paper would provide a lower-dimensional analogue of known (3+1)-dimensional results: holography holds for flat/open FRW universes and is violated by negative curvature/negative cosmological constant phases. Such a demonstration could be a useful check of cosmic holography in simpler settings. The paper also usefully assembles the relevant literature, including the Wang-Abdalla and Kaloper-Linde analyses. However, the load-bearing derivations contain algebraic errors and the observational section does not actually constrain the proposed model, so the central conclusions are not supported as written.

major comments (4)
  1. [Sec. 3.1, Eq. (13)] Eq. (13) is inconsistent with Eqs. (11)–(12). From Eq. (11), L_H = a r_H, and from Eq. (12), r_H = (1/√D) ln(a/a0) with D=2Gβ0−k. Therefore S/A = σ L_H/a^2 = σ r_H/a = σ ln(a/a0)/(a√D), not σ√D (a/a0). The printed expression grows with a, whereas the correct expression is non-monotonic: it starts at zero (a=a0), rises to a maximum at a=e a0, and then decays. The text's conclusion that the bound is automatically maintained in expanding flat/open universes therefore does not follow. This error directly affects the paper's main claim.
  2. [Sec. 3.2, Eqs. (14)–(15)] For radiation with ρ=2p (ζ=3/2, ρ0=0), the conservation equation (6) gives ρa^3=const, not ρa^2=const. Equation (14) reads ρa^2=const=d0 a0^3, which is dimensionally inconsistent (the constant on the left and the right side have different powers of a0) and also inconsistent with Eq. (15), where the term 2Gβ0/a follows only if β0∝d0 a0^3 and ρ∝a^{-3}. The printed Eq. (14) must be a typo, but as it stands it invalidates the derivation of the radiation-era scale factor and of the S/A∼t^{-1/3} result in Sec. 3.3.
  3. [Sec. 4, Eqs. (23)–(26)] The treatment of the flat model with λ<0 is internally confused. In Eq. (23), the term is −λa^2. If λ<0, this term is positive and supports eternal expansion, not recollapse; to obtain a turning point one needs λ>0 with the sign convention of Eq. (23). The text nevertheless describes a collapse for λ<0. Moreover, the exponent in Eq. (26), S/A∼σλ^{1/(ζ−1/2)}, is inconsistent with the preceding line, which states S/A∼σλ^{1/ζ−1/2}. These inconsistencies make the claimed violation after the turning point unverifiable.
  4. [Secs. 5–6, Figs. 1–7] The observational analysis does not test the model. The theoretical H(z) curves in Figs. 1–7 are those of flat ΛCDM, H(z)=H0√(Ωm(1+z)^3+1−Ωm), with no mapping to the parameters ζ, ρ0, λ, or B0 of the generalized equation of state. The MCMC contours in Fig. 7 are therefore constraints on ΛCDM parameters, not on the model proposed in this paper. The conclusion that the model is 'observationally viable' is not supported by the presented analysis.
minor comments (4)
  1. [Throughout] There are numerous typos and inconsistent terms: 'harmonic principle' instead of 'holographic principle' (twice in the Introduction), 'FLR W' spacing, 'ans hence' in Sec. 3.3, 'Monte Carlo Markov chain' instead of 'Markov Chain Monte Carlo', and 'Table of 30 points' with no table provided.
  2. [Sec. 3.4] The closed-universe discussion is qualitative and relies on Refs. [22,23] without presenting the equations or the turning-point calculation. As written it is not a derivation.
  3. [Data Availability] The Data Availability Statement says 'The paper does not include any data,' but the paper uses 30 observational Hubble data points and presents them in figures. This should be corrected.
  4. [References] Some references have incomplete or possibly incorrect metadata, e.g., Ref. [3] and Ref. [5] share the same page/article title but are different works, and Ref. [24] gives inconsistencies in volume/page numbers. Please verify all entries.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the holography check is imported from external references and the observational fit is not the holography derivation; the main issues are mathematical inconsistencies, not circular reasoning.

full rationale

The paper's central holography analysis is not circular in the sense of fitting a quantity and then predicting it. The entropy convention S = σ L_H and area A = a^2 are taken from Wang and Abdalla [22], and the closed/λ<0 method is taken from Kaloper and Linde [2]; these are external references, not self-citations. The observational section fits ΛCDM H0 and Ωm to Hubble data, which is unrelated to the generalized equation-of-state model used in the holography sections, but this is a validity/mismatch problem, not circularity. There is one minor self-citation: [25] (Khadekar, Kumar, Islam, with coauthor S. Islam) is cited for the standard (2+1)-dimensional FLRW line element and conservation equation; this is not load-bearing because those equations are standard. The main derivation contains algebraic inconsistencies—Eq. (13) does not follow from Eqs. (11)–(12), and the radiation scaling in Eq. (14) is inconsistent with the subsequent equation—but these are correctness errors, not circular reductions. The score of 2 reflects only the minor, non-load-bearing self-citation; the central claim is not forced by definition or by a self-citation chain.

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

The central derivation has two free parameters from the equation of state plus a hand-selected lambda regime, and the claimed observational support comes from fitting Lambda-CDM parameters that are not parameters of the model being tested. The entropy-bound identification and the statistical model are imported from prior literature.

free parameters (5)
  • zeta = not reported
    Free parameter in the generalized equation of state Eq. (7). No best-fit value is derived or quoted in the paper.
  • rho0 = not reported
    Free parameter in Eq. (7). Assumed negative in Section 4 to produce lambda<0, but never constrained by observational data.
  • lambda = not reported (regime lambda<0 assumed)
    Effective negative-cosmological-constant-like parameter in Eq. (23). Its sign and magnitude are chosen by hand; the intro's formula lambda=2(gamma-1)^2/gamma is never connected to the body.
  • H0 = 68.16 km/s/Mpc
    Fitted using chi-square minimization to 30 Hubble data points in Section 5, but for a Lambda-CDM model, not for the generalized equation of state.
  • Omega_m = 0.32
    Fitted alongside H0 in the same Lambda-CDM analysis. It is not a parameter of the holographic model in Eqs. (7) or (23).
assumptions (4)
  • domain assumption Einstein field equations in (2+1) dimensions take the form G_{ij}=2 pi G T_{ij} as in Eq. (2), citing Ref. [24].
    The entire Friedmann system in Section 2 rests on this dimension-specific field equation, taken from prior literature without independent derivation.
  • ad hoc to paper The matter content is a single perfect fluid with generalized linear equation of state p=(zeta-1)(rho+rho0), Eq. (7).
    This equation of state is introduced specifically for this analysis; there is no external observational or microphysical justification given for it.
  • domain assumption The holographic bound in (2+1) dimensions is S/A = sigma L_H / a^2 with particle horizon L_H as defined in Eqs. (11)-(13), following Ref. [22].
    The conclusion that flat/open universes satisfy the bound and closed universes violate it depends on this specific entropy-area identification.
  • domain assumption The 30 Hubble measurements are independent and have Gaussian errors sigma_H(z_i) as used in the chi-square statistic Eq. (27).
    No covariance matrix, systematic error model, or data table is provided, so the reported fit assumes this statistical model.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Observational constraints on holography in $(2 + 1)$-dimensional cosmology with a generalized equation of state." pith.science (2026). https://pith.science/paper/O3ABIWYO

@misc{pith2026250811701,
  author       = {Pith},
  title        = {Pith review of: Observational constraints on holography in $(2 + 1)$-dimensional cosmology with a generalized equation of state},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/O3ABIWYO}},
  note         = {Machine review of arXiv:2508.11701}
}
abstract

In this study we explore the cosmic holographic principle, as proposed by Fischler and Susskind~\cite{Fischler}, within the framework of $(2 + 1)$-dimensional cosmological models. A generalized equation of state is employed, given by $p = (\zeta - 1)(\rho + \rho_0)$, where $\zeta$ and $\rho_0$ are treated as two free parameters. The analysis confirms the validity of the holographic principle in all flat and open universes. However, for a $(2 + 1)$-dimensional closed universe, we apply the method proposed by Kaloper and Linde~\cite{Kaloper}, and observe that the holographic principle is generally not satisfied. Furthermore, we examine the stability of the proposed model using the Markov chain Monte Carlo (MCMC) method, and estimate the best-fit values for the model parameters based on observational Hubble data sets.

Figures

Figures reproduced from arXiv: 2508.11701 by the authors.

Figure 1
Figure 1. The plot of Hubble parameter H(z) vs redshift z for the theoretical curves for different values of matter density parameter Ωm = 0.2, 0.3, 0.4 and the blue dots depict the 30 points of the Hubble observational dataset [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. The plot of Hubble parameter H(z) vs redshift z for different values of H0 = 65, 70, 75 (in the unit km/s/Mpc) [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. The plot between Hubble parameter H(z) versus redshift z for different values of matter density parameter Ωm = 0.2, 0.3, 0.4 [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: The plot for Best fit of Hubble parameter [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: The plot of Residuals of Hubble parameter versus redshift [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: The plot of relative difference between observed and theoretical Hubble parameter versus [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: The contour plot for the confidence regions for [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

35 extracted references · 33 canonical work pages

  1. [1]

    Fischler, L

    W. Fischler, L. Susskind, Holography and Cosmology, arXiv:hep-th/9806039

    arXiv

  2. [2]

    Kaloper, A

    N. Kaloper, A. Linde, Cosmology vs. Holography, Phys. Rev. D 60 (1999) 103509

    work page 1999

  3. [3]

    Giddings, J

    S. Giddings, J. Abbott, K. Kucar, Einstein theory in a three dimensional spacetime, Gen. Rel. Grav. 16 (1984) 751

    work page 1984

  4. [4]

    Barrow, A.B

    J.D. Barrow, A.B. Burd, D. Lancaster, Three dimensional classical spacetime, Class. Quantum Grav. 3 (1986) 551

    work page 1986

  5. [5]

    Gott, J.Z

    J.R. Gott, J.Z. Simon, M. Alpert, General relativity in a (2 + 1)-dimensional space- time: An electrically charged solution, Gen. Rel. Grav. 16 (1984) 751

    work page 1984

  6. [6]

    Deser, R

    S. Deser, R. Jackiw, G. t’Hooft, Three dimensional Einstein gravity: dynamics of flat space, Ann. Phys. NY 152 (1984) 220

    work page 1984

  7. [7]

    Deser, P

    S. Deser, P. Mazur, Static solution in D=3 Einstein Maxwell theory, Class. Quantum Grav. 2 (1985) L51

    work page 1985

  8. [8]

    Deser, Relativity, Cosmology, Topological Mass and SUGR, ed C Aragone (Sin- gapore: World Scientific)

    S. Deser, Relativity, Cosmology, Topological Mass and SUGR, ed C Aragone (Sin- gapore: World Scientific)

    work page

Show all 35 references
  1. [9]

    Banados, C

    M. Banados, C. Teitelboim, J. Zanelli, Black hole in three dimensional spacetime, Phys. Rev. Lett. 69 (1992) 1849

    1992

  2. [10]

    Barrow, D.J

    J.D. Barrow, D.J. Shaw, C.G. Tsagas, Cosmology in three dimensions: steps towards the general solution, Class. Quantum Grav. 23 (2003) 124022

    2003

  3. [11]

    Garica, M

    A. Garica, M. Cataldo, S. del Compo, Relation between (2 + 1) and (3 + 1) Freidmann-Robertson-Walker cosmologies, Phys. Rev. D 68 (1999) 103509

    1999

  4. [12]

    X.H. Meng, P. Wang, Modified Friedmann equations R−1 -modified gravity, Class. Quantum Grav. 20 (2003) 4949

    2003

  5. [13]

    Babichev, V

    E. Babichev, V. Dokuchaev, Yu. Eroshenko, Dark energy cosmology with generalized linear equation of state, Class. Quantum Grav. 22 (2005) 143

    2005

  6. [14]

    t’Hooft, Published in Salam-festschrift: a collection of talks, In: Ali, A., Ellis, J., Randjibar-Daemi, S

    G. t’Hooft, Published in Salam-festschrift: a collection of talks, In: Ali, A., Ellis, J., Randjibar-Daemi, S. (eds.) Word Scientific. arXiv:gr-qc/9310026

    arXiv

  7. [15]

    Susskind, The world as a hologram, J

    L. Susskind, The world as a hologram, J. Math. Phys. 36 (1995) 6377

    1995

  8. [16]

    Rama, Holographic principle in the closed universe: a resolution with negative pressure matter

    S.K. Rama, Holographic principle in the closed universe: a resolution with negative pressure matter. Phys. Lett. B 457 (1999) 268

    1999

  9. [17]

    Bak, S.J

    D. Bak, S.J. Rey, Cosmic holography, Class. Quantum. Grav. 17 (2000) L83

    2000

  10. [18]

    Biswas, J

    A.K. Biswas, J. Maharana, R.K. Pradhan, The holography hypothesis and pre-big bang cosmology, Phys. Lett. B 462 (1999) 243

    1999

  11. [19]

    Veneziano, Pre-Big-bang origin of our entropy and time arrow, Phys

    G. Veneziano, Pre-Big-bang origin of our entropy and time arrow, Phys. Lett. B 454 (1999) 22

    1999

  12. [20]

    Kaloper, A

    N. Kaloper, A. Linde, R. Bousso, Pre-Big-Bang requires the universe to be expo- nentially large from the very beginning, Phys. Rev. 59 (1999) 043508

    1999

  13. [21]

    X.H. Meng, J. Ren, M.G. Hu, Friedmann cosmology with generalized equation of state and bulk viscosity, Commu. Theor. Phys. 47 (2007) 378

    2007

  14. [22]

    B. Wang, E. Abdalla, Holography in (2 + 1)-dimensional cosmological models, Phys. Lett. B 466 (1999) 122

    1999

  15. [23]

    B. Wang, E. Abdalla, Holography and generalized second law of thermodynamics in (2+1)-dimensional cosmology, Phys. Lett. B 471 (2000) 346

    2000

  16. [24]

    Cornish, N.E

    N.J. Cornish, N.E. Frankel, Gravitation in (2 + 1)-dimensions. Phys. Rev. D 43 (2000) 2555

    2000

  17. [25]

    Khadekar, P

    G.S. Khadekar, P. Kumar, S. Islam, Modified Chaplygin gas with bulk viscous cosmology in FR W (2+ 1)-dimensional spacetime, J. Astrophys. Astron.40(5), 40 (2019)

    2019

  18. [26]

    Bousso, A covariant entropy conjecture, JHEP 9907 (1999) 004

    R. Bousso, A covariant entropy conjecture, JHEP 9907 (1999) 004

    1999

  19. [27]

    Bousso, Holography in general space, JHEP 9906 (1999) 028 September 8, 2025 12:30 ThakranEtAl˙Holography˙IJGMMP˙12-08-2025˙Arxiv 13

    R. Bousso, Holography in general space, JHEP 9906 (1999) 028 September 8, 2025 12:30 ThakranEtAl˙Holography˙IJGMMP˙12-08-2025˙Arxiv 13

    1999

  20. [28]

    H. Yu, B. Ratra, F.Y. Wang, Hubble Parameter and Baryon Acoustic Oscillation Measurement Constraints on the Hubble Constant, the Deviation from the Spatially Flat ΛCDM Model, the Deceleration–Acceleration Transition Redshift, and Spatial Curvature Astrophys. J. 3 (2018) 856

    2018

  21. [29]

    Moresco, Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z ∼ 2 Mon

    M. Moresco, Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z ∼ 2 Mon. Not. R. Astron. Soc.450 (2015) L16–L20

    2015

  22. [30]

    Khadekar, A

    G.S. Khadekar, A. Ghogre, Bulk viscosity in Friedmann universe with a varying speed of light described by modified equation of state, Int. J. Geom. Meth. Mod. Phys. 12(10) (2015) 1550126

    2015

  23. [31]

    Khadekar, Inhomogeneous early viscous fluid universe: A concrete model for dark energy, Int

    G.S. Khadekar, Inhomogeneous early viscous fluid universe: A concrete model for dark energy, Int. J. Geom. Meth. Mod. Phys.13(04) (2016) 1650037

    2016

  24. [32]

    Chattopadhyay, A study on the bouncing behavior of modified Chaplygin gas in presence of bulk viscosity and its consequences in the modified gravity framework, Int

    S. Chattopadhyay, A study on the bouncing behavior of modified Chaplygin gas in presence of bulk viscosity and its consequences in the modified gravity framework, Int. J. Geom. Meth. Mod. Phys.14(12) (2017) 1750181

    2017

  25. [33]

    Debnath, B.C

    P.S. Debnath, B.C. Paul, Observational constraints of emergent universe in f (R, T) gravity with bulk viscosity, Int. J. Geom. Meth. Mod. Phys.17(07) (2020) 2050102

    2020

  26. [34]

    Sadatian, S.M.R

    S.D. Sadatian, S.M.R. Hosseini, Symmetric teleparallel gravity f (Q, T) and anisotropic bulk viscosity, Int. J. Geom. Meth. Mod. Phys.22(04) (2025) 2450308

    2025

  27. [35]

    Mazumdar, M.M

    R. Mazumdar, M.M. Gohain, K. Bhuyan, Cosmological bounce scenario with a novel parametrization of bulk viscosity, Int. J. Geom. Meth. Mod. Phys.22(03) (2025) 2450292

    2025

Pith tools

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