Pith. sign in

REVIEW 4 major objections 5 minor 51 references

Exploring the effects of dark matter - dark energy interaction on cosmic evolution in viscous dark energy scenario

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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

Pith's one-line read The paper claims that a generalized viscous interacting dark energy model fits Union 2.1 supernova data and returns a mildly phantom equation of state near $\omega_{\rm de} \approx -1.07$, along with small but nonzero dark-sector coupling…

desk verdict The MCMC headline numbers rest on a Hubble law that the paper never derives and that does not follow from the model's own equations; until that is fixed, the central result is not reproducible. read the letter →

arxiv 2411.13379 v1 pith:AJOPOEWV submitted 2024-11-20 astro-ph.CO gr-qchep-ph

Ashadul Halder , Madhurima Pandey , Rupa Basu , Debasish Majumdar This is my paper · ORCID
classification astro-ph.COgr-qchep-ph PACS 95.36.+x95.35.+d98.80.-k
keywords darkmatter-darkenergyinteractionbulkviscosityviscousinteractingcosmicaccelerationUnion2.1supernovaeMarkovChainMonteCarloOm3diagnostic
topics Dark Energy
open problems Dark MatterDark 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

The paper tries to establish that the cosmic expansion history can be described by a dark energy fluid that is both bulk-viscous and interacting with dark matter, and that this combination is visible in supernova data. To do so it proposes a generalized interacting dark energy model whose coupling constants are packaged into a strength $\lambda_r$ and a mixing angle $\lambda_\theta$, and it takes the dark energy viscosity to be proportional to the Hubble rate. Fitting the resulting Hubble parameter to the Union 2.1 Type Ia supernova sample with Markov Chain Monte Carlo, the paper reports best-fit values $h_0 = 0.68$, $\lambda_r = 0.09$, $\lambda_\theta = 0.41$, $\omega_{\rm de} = -1.07$, $\Omega_{k,0} = 0.10$, and $\eta = 0.05$. A sympathetic reader would take this as evidence that the data mildly prefer a phantom-like dark energy with a small viscous coefficient and a nonzero dark-sector coupling. The paper also shows that viscosity and the interaction move the deceleration, jerk, snap, and Om/Om3 diagnostics away from the $\Lambda$CDM behavior, with viscosity playing the most visible role.

What carries the argument

The central object is the generalized Hubble parameter for interacting viscous dark energy, written in equation (16) as a modification of the viscous dark energy expression (15), with the interaction entering through the transfer $Q = 3H(\lambda_{\rm de}\rho_{\rm de} + \lambda_\chi\rho_\chi)$. This quantity carries the argument because it is used both to compute the distance moduli compared with Union 2.1 data and to generate the evolution of density parameters and the higher-order diagnostics. The model's six free parameters are the present Hubble constant $h_0$, the coupling strength $\lambda_r$, the coupling mixing angle $\lambda_\theta$, the dark energy equation of state $\omega_{\rm de}$, the curvature density $\Omega_{k,0}$, and the dimensionless viscosity $\eta$ defined through $\zeta = \eta H$. The diagnostics side uses the Om parameter and the three-point Om3 statistic as null tests against $\Lambda$CDM.

What would settle it

Recompute the distance moduli from equations (1), (2), (3), and (16) using the reported best-fit parameters and compare them with the Union 2.1 likelihood; if the resulting posteriors differ from Figure 7, the stated parameters are not the model's actual best fit. A simpler check is to solve the coupled density equations numerically with the reported parameters and verify that the Hubble parameter used in the analysis is recovered.

Watch

Extended reading notes

Core claim

The central discovery the paper argues for is that a single generalized model, obtained by writing the dark-sector energy transfer as $Q = 3H(\lambda_{\rm de}\rho_{\rm de} + \lambda_\chi \rho_\chi)$ and parametrizing the couplings by $\lambda_\chi = \lambda_r \sin\lambda_\theta$ and $\lambda_{\rm de} = \lambda_r \cos\lambda_\theta$, can reproduce the observed distance-redshift relation once dark energy is given a bulk viscosity $\zeta = \eta H$. With the Union 2.1 data the MCMC fit returns $h_0 = 0.68$, $\lambda_r = 0.09$, $\lambda_\theta = 0.41$, $\omega_{\rm de} = -1.07$, $\Omega_{k,0} = 0.10$, and $\eta = 0.05$. The paper presents this as a mildly phantom dark energy with small viscosity and nonzero coupling, and it claims that the resulting model produces characteristic deviations from $\Lambda$CDM in the density-parameter evolution and in the $q$, $j$, $s$, and Om/Om3 diagnostics. It also notes that the curvature parameter has little dynamical effect and that lower interaction strengths are preferred.

Load-bearing premise

The load-bearing premise is that the Hubble parameter actually used in the MCMC fit follows from the model's coupled dark matter and dark energy density equations; the paper never displays the evolution of $\rho_\chi$ and $\rho_{\rm de}$ that would turn equation (16) into concrete distance moduli, so the fit could in principle be disconnected from the stated physics.

Editorial extensions

If this is right

  • If the best-fit parameters are right, the present acceleration is driven by a mildly phantom dark energy ($\omega_{\rm de} \approx -1.07$) with a small bulk viscosity ($\eta \approx 0.05$) and a weak but nonzero dark-sector coupling ($\lambda_r \approx 0.09$).
  • The model predicts that increasing viscosity slows the late-time expansion, so precise measurements of $H(z)$ around $z \lesssim 2$ could distinguish a viscous contribution from a pure cosmological constant.
  • The Om3 diagnostic, which is a constant unity for $\Lambda$CDM, is expected to dip below unity at higher redshifts and approach quintessence-like values at low redshifts, a signature that can be searched for in independent expansion data.
  • Because lower $\lambda_r$ values are preferred and the curvature posterior is nearly flat, the model anticipates that future distance data will tighten the dark-sector coupling while leaving $\Omega_{k,0}$ poorly constrained.

Reading between the lines

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

  • A natural extension would be to re-run the same generalized model on the Pantheon+ or DES-SN samples; those data sets would show whether the mildly phantom value $\omega_{\rm de} \approx -1.07$ is a Union 2.1 artifact or a stable feature of viscous interacting dark energy.
  • The missing density evolution can be supplied by numerically integrating the coupled ODEs; such an independent computation would either reproduce the reported best fit or expose the degree to which the printed Hubble parameter is approximate.
  • The parametrization in terms of $\lambda_r$ and $\lambda_\theta$ invites a physical reading: the ratio $\lambda_\chi/\lambda_{\rm de} = \tan\lambda_\theta$ determines whether dark matter or dark energy is the dominant receiver of the energy transfer, and the posterior's broad peak near $7\pi/10$ suggests the data favor a transfer dominated by the dark energy coupling.
  • To break degeneracies among $\omega_{\rm de}$, $\eta$, and $\lambda_r$, a joint fit that adds CMB and BAO data would be needed; the present single-probe analysis cannot separate these effects.
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 / 5 minor

Summary. The paper proposes a generalized interacting dark energy (IDE) model with a two-parameter coupling Q = 3H(λdeρde + λχρχ), parameterized by λχ = λr sin λθ and λde = λr cos λθ, in a bulk-viscous dark energy framework with ζ = ηH. It presents three viscous dark energy Hubble expressions, a generalized form, and then an 'interacting' Hubble expression (Eq. 16). Using that expression, the authors compute deceleration, jerk, snap, Om and Om3 diagnostics, and perform an MCMC fit to the Union 2.1 supernova dataset, reporting optimum parameters h0 = 0.68, λr = 0.09, λθ = 0.41, ωde = −1.07, Ωk0 = 0.10, η = 0.05. The central quantitative claim is that this interacting viscous model fits the data and yields mildly phantom dark energy with small dark-sector coupling.

Significance. If the model and fit were correctly derived and reproducible, the paper would offer a useful two-parameter unification of common IDE interaction forms and a first constraint on their combination with bulk viscosity. That would be of interest to the dark-energy phenomenology community. However, the central Hubble expression used in the likelihood is never derived or closed, the viscous-pressure definition is internally inconsistent, and the MCMC analysis reports no goodness-of-fit or model comparison. As presented, the paper does not deliver reliable constraints on the interaction or viscosity parameters. It also provides no code, data products, or machine-checked derivations, so the quantitative claims cannot be independently verified.

major comments (4)
  1. [III, Eq. (16); IV, MCMC fit] Equation (16), which is the only Hubble law entering the Union 2.1 likelihood, is not closed and does not follow from the stated model. The quantities ρχ and ρde appear without evolution equations or a specification of whether they are present-day densities or redshift-dependent functions; as written, the expression cannot be differentiated or integrated to distance moduli. Solving the continuity equations (1)-(2) with the interaction (3) and the viscous pressure (11) in a flat two-fluid system yields a coupled linear system whose solution is a superposition of two power laws, not the factored form of Eq. (16). Furthermore, Eq. (16) does not reduce to the noninteracting limit Eq. (15): the dark-energy term in Eq. (16) scales as (1+z)^{-3η} and lacks the factor (1+z)^{3(1+ωde)} present in Eq. (15), so the two expressions agree only for special parameter values, not for the quoted best fit ωde = −1.07. The reported parameters h0 = 0.68, λr = 0.09, λθ = 0.41, ωde = −1.07, Ωk0 = 0.10, η = 0.05 are therefore not attached to a well-defined model, and the fit cannot be reproduced or checked.
  2. [III, Eqs. (9) and (11)] The definition of the viscous pressure is internally inconsistent. Equation (9) states pde = ωdeρde = ζθ, while Eq. (11) gives pde = ωdeρde − 3ηH²; with ζ = ηH and θ = 3H these two expressions differ by the sign of the viscous term. The viscous contribution in Eq. (11) is the physically expected −ζθ, so Eq. (9) is not merely a notation issue but a contradictory definition of pde. Since η enters all subsequent Hubble expressions (12)-(16) through this pressure, the derivation of the three VDE models rests on an ill-defined equation.
  3. [IV, MCMC paragraph and Table III] The MCMC fit is underspecified and its output is not assessed. Equation (16) contains Ωb0, which is not listed in Table III or given anywhere, and the value of Ωm0 used in the likelihood is never reported; without these values the distance moduli cannot be reproduced. In addition, the paper reports only the posterior peak and contour plots. It gives no χ², no log-evidence, no comparison with ΛCDM or with the noninteracting VDE models (12)-(14), and no goodness-of-fit statistic. The conclusion that the generalized interacting model is favored—or even that the fit is acceptable—is therefore unsupported by the presented evidence.
  4. [IV, Eq. (23)] The three-point diagnostic is misdefined. With Om(z2,z1) = [h²(z2) − h²(z1)]/[(1+z2)³ − (1+z1)³] and Om(z3,z1) = [h²(z3) − h²(z1)]/[(1+z3)³ − (1+z1)³], the ratio Om(z2,z1)/Om(z3,z1) has h²(z3) − h²(z1) in the denominator, not h²(z3) − h²(z2) as written in Eq. (23). The plotted Om3 curves and the phantom/quintessence interpretation in Fig. 3(b) are therefore based on an incorrect formula.
minor comments (5)
  1. [II, first paragraph] The text says the three benchmark models are considered to investigate the effect of DM-DE interaction on brightness temperature, but the paper contains no brightness-temperature analysis; this appears to be a leftover from a different study.
  2. [IV, Fig. 2(a) discussion] The sentence 'the black and green solid lines represent the evolution of dark matter density parameter Ωde' is confusing: the notation Ωde is the dark energy density parameter, not dark matter, and the accompanying text should distinguish Ωde, Ωχ, Ωb, and Ωrad clearly.
  3. [IV, MCMC paragraph] The text says the topmost plots in the first, second, third, and fourth columns of Figure 7 represent six parameters (h0, λr, λθ, ωde, Ωk0, η) respectively, which is arithmetically inconsistent; the posterior peak for λθ is also quoted as both λθ = 0.41 and λθ ≈ 7π/10, and these two values are not compatible.
  4. [IV, after Eq. (19)] There is a stray '.' line immediately after the definition of the snap parameter, which should be removed.
  5. [Figures 5 and 6] The figures display Mathematica-style output artifacts (e.g., 'Out[27]=', 'Out[33]=', 'Out[39]=', 'Out[45]=' in the captions), and the λθ axis ticks are displayed in radians without a label; these should be cleaned for publication.

Circularity Check

2 steps flagged · score 6.0 of 10

The 'phantom' diagnosis is just the fitted omega_de rewritten through Om/Om3, and the generalized Hubble law used in the fit is a self-cited 'model agnostic' ansatz rather than a solved consequence of the interacting-viscous equations.

  1. ansatz smuggled in via citation [Section III, Eq. (15)-(16); Section V conclusion; Abstract ('model agnostic form of VDE')]
    "The evolution equation of Hubble parameters due to different VDE models can also be acquired from a generalized expression as introduced in [32]. ... we consider a model agnostic form of VDE. ... we adopt a generalized form of the Hubble parameter for the VDE scenario, as introduced in one of our previous works [32]"

    The Hubble law that feeds the MCMC likelihood is not derived from the stated conservation equations (1)-(3) and (10)-(11); it is declared 'can be written as' in Eq. (15) and 'takes the form' in Eq. (16). Its only cited source is the authors' own previous work [32], and the paper itself labels the construction 'model agnostic.' The fit therefore evaluates an assumed parametrization imported via self-citation, and the expansion history that is 'predicted' is the ansatz evaluated at fitted parameters, not a solution of the model equations.

  2. fitted input called prediction [Section IV, Eq. (21)-(23) and MCMC paragraph; Figures 3-4]
    "We conduct a Bayesian analysis to compare our model with the Union 2.1 supernova Ia data. To perform this comparison, we calculate the distance modulus using standard cosmological distance relations incorporating the proposed cosmological model. ... Om(z2, z1) = h2(z2) − h2(z1) / ((1 + z2)3 − (1 + z1)3)"

    The distance modulus is built from the same h(z) = H(z)/H0 that is fitted, and Om/Om3 in Eqs. (21)-(23) are defined directly from that fitted h(z). The paper reads Om3 < 1 as evidence for phantom dark energy, but omega_de is itself one of the fitted parameters (omega_de = -1.07). The diagnostic is therefore a re-plotting of the fitted expansion history, not an independent test; the 'prediction' of phantom behavior reduces by construction to the value already fitted to the Union 2.1 likelihood.

full rationale

The parameter estimation itself is a legitimate fit to an external dataset, so I do not score it as fully circular. The circularity enters in two places. First, the generalized Hubble law (Eqs. 15-16) is an assumed, 'model agnostic' form whose stated external origin is the authors' own [32]; because the paper never solves the coupled interacting-viscous equations to obtain this H(z), the fitted model is the imported ansatz rather than the physical model of Section II. Second, the diagnostic claims (phantom behavior from Om3 and the q/j/s evolutions) are computed from the same fitted h(z) and thus carry no independent information about omega_de. A separate, non-circularity correctness issue should be flagged: Eq. (16) is not closed, since the evolution of rho_chi and rho_de is never specified and the interaction parameters lambda_r, lambda_theta do not visibly enter the fitted Hubble law, so the reported lambda constraints may be priors rather than data-driven. That missing derivation lowers confidence but is not itself a circular reduction; for that reason the score is 6 rather than 8-10.

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

The central result is a numerical fit of six parameters to one supernova dataset. No external benchmark is used: the Hubble parameter is constructed from the model's own assumptions and then fitted to distance moduli. The key missing ingredient is the solution of the coupled DM-DE conservation equations for the interacting viscous case, which would be a derivation input; the paper instead leaves Eq. (16) unclosed. No new particles or new physical entities are introduced.

free parameters (6)
  • h0 = 0.68+0.03-0.03
    Present-day Hubble constant, fitted to Union 2.1 supernova data.
  • lambda_r = 0.09+0.07-0.06
    Interaction strength in Q=3H(lambda_de rho_de + lambda_chi rho_chi); fitted to SNe data.
  • lambda_theta = 0.41+1.86-2.07
    Mixing angle setting lambda_chi=lambda_r sin(lambda_theta) and lambda_de=lambda_r cos(lambda_theta); posterior is broad and the text notes the peak is near 7pi/10.
  • omega_de = -1.07+0.25-0.27
    Dark energy equation of state parameter, fitted to supernova distances.
  • Omega_k0 = 0.10+0.07-0.07
    Curvature density parameter, fitted within the prior range [0,0.2]; the posterior is flat, so it is poorly constrained.
  • eta = 0.05+0.13-0.14
    Bulk viscosity coefficient in zeta=eta H; fitted to SNe data and consistent with zero at about 1 sigma.
assumptions (5)
  • standard math FRW metric and Friedmann equations with 8piG=c=hbar=1 are the background framework.
    Invoked throughout Section III in deriving the Hubble parameter and density evolution.
  • domain assumption Eckart's first-order viscous theory with zero relaxation time and effective pressure pde=omega_de rho_de - 3 eta H^2.
    Assumed in Eqs. (9)-(11); the bulk viscosity is set proportional to H (zeta=eta H), an ad hoc choice not derived from microphysics.
  • ad hoc to paper The DM-DE interaction takes the form Q=3H(lambda_de rho_de + lambda_chi rho_chi) with lambda_chi=lambda_r sin(lambda_theta), lambda_de=lambda_r cos(lambda_theta).
    Eqs. (3)-(5). This parametrization is introduced to unify three benchmark models but restricts the coupling space and is not observationally motivated.
  • domain assumption Radiation contribution is neglected; curvature is included only in some models.
    Stated after Eq. (12); plausible for low-redshift SNe fitting but an approximation.
  • ad hoc to paper The matter density parameter Omega_m0 is fixed rather than fitted in the MCMC analysis, but its value is not explicitly reported.
    Figure 3(a) indicates Omega_m0 about 0.31 in the Lambda-CDM curve, but the MCMC section does not state how Omega_m0 is set or marginalized.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Exploring the effects of dark matter - dark energy interaction on cosmic evolution in viscous dark energy scenario." pith.science (2026). https://pith.science/paper/AJOPOEWV

@misc{pith2026241113379,
  author       = {Pith},
  title        = {Pith review of: Exploring the effects of dark matter - dark energy interaction on cosmic evolution in viscous dark energy scenario},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AJOPOEWV}},
  note         = {Machine review of arXiv:2411.13379}
}
abstract

We explore the influence of interactions between dark matter (DM) and dark energy (DE) on the cosmic evolution of the Universe within a viscous dark energy (VDE) framework. Moving beyond traditional interacting dark energy (IDE) models, we propose a generalized IDE model adaptable to diverse IDE scenarios via IDE coupling parameters. In order to investigate deviations from $\Lambda$CDM across cosmic epochs by highlighting how viscous and the interactions between DM and DE impact cosmic density and expansion rates, we consider a model agnostic form of VDE. Eventually we perform a Bayesian analysis using the Union 2.1 Supernova Ia dataset and Markov Chain Monte Carlo (MCMC) sampling to obtain optimal values of model parameters. This comprehensive analysis provides insights about the interplay between viscous and IDE in shaping the Universe's expansion history.

Figures

Figures reproduced from arXiv: 2411.13379 by the authors.

Figure 1
Figure 1. FIG. 1. Variation of Hubble evolution ( [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) Evolution of density parameters with redshift [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) Evolution of [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Variation of (a) [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. (a) Variation of deceleration parameter ( [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Variation of deceleration parameter ( [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Corner plot showing the MCMC result for our model carried out using the observational results of Union 2.1 supernova [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

51 extracted references · 39 canonical work pages

  1. [1]

    A. G. Riess, A. V. Filippenko, P. Challis, A. Clocchiatti, A. Diercks, P. M. Garnavich, R. L. Gilliland, C. J. Hogan, S. Jha, R. P. Kirshner, B. Leibundgut, M. M. Phillips, D. Reiss, B. P. Schmidt, R. A. Schommer, R. C. Smith, J. Spyromilio, C. Stubbs, N. B. Suntzeff, and J. Tonry, Observational evidence from supernovae for an accelerating universe and a ...

    work page 1998

  2. [2]

    Perlmutter, M

    S. Perlmutter, M. S. Turner, and M. White, Constraining dark energy with type ia supernovae and large-scale structure, Phys. Rev. Lett. 83, 670 (1999)

    work page 1999

  3. [3]

    D. H. Weinberg, M. J. Mortonson, D. J. Eisenstein, C. Hirata, A. G. Riess, and E. Rozo, Observational probes of cosmic acceleration, Phys. Rep. 530, 87 (2013), arXiv:1201.2434 [astro-ph.CO]

    arXiv 2013

  4. [4]

    C. L. Bennett et al., Nine-year wilkinson microwave anisotropy probe (wmap) observations: Final maps and results, Astrophys. J. Suppl. Ser. 208, 20 (2013)

    work page 2013

  5. [5]

    Collaboration, Planck 2013 results

    P. Collaboration, Planck 2013 results. XVI. Cosmological parameters, Astron. Astrophys.571, A16 (2014), arXiv:1303.5076 [astro-ph.CO]

    arXiv 2014

  6. [6]

    Collaboration, Planck 2015 results

    P. Collaboration, Planck 2015 results. XIII. Cosmological parameters, Astron. Astrophys. 594, A13 (2016), arXiv:1502.01589 [astro-ph.CO]

    arXiv 2016

  7. [7]

    Weinberg, The cosmological constant problem, Rev

    S. Weinberg, The cosmological constant problem, Rev. Mod. Phys. 61, 1 (1989)

    1989

  8. [8]

    Zlatev, L

    I. Zlatev, L. Wang, and P. J. Steinhardt, Quintessence, cosmic coincidence, and the cosmological constant, Phys. Rev. Lett. 82, 896 (1999)

    work page 1999

Show all 51 references
  1. [9]

    J. S. Bullock and M. Boylan-Kolchin, Small-Scale Challenges to the ΛCDM Paradigm, Annu. Rev. Astron. Astrophys. 55, 343 (2017), arXiv:1707.04256 [astro-ph.CO]

    2017 arXiv

  2. [10]

    A. G. Riess, The Expansion of the Universe is Faster than Expected, Nature Rev. Phys. 2, 10 (2019), arXiv:2001.03624 [astro-ph.CO]

    2019 arXiv

  3. [11]

    A. G. Riess, S. Casertano, W. Yuan, L. M. Macri, and D. Scolnic, Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyondλcdm, The Astrophysical Journal 876, 85 (2019)

    2019

  4. [12]

    K. C. Wong et al., H0LiCOW - XIII. A 2.4 per cent measurement of H 0 from lensed quasars: 5.3 σ tension between early- and late-Universe probes, Mon. Not. Roy. Astron. Soc. 498, 1420 (2020), arXiv:1907.04869 [astro-ph.CO]

    2020 arXiv

  5. [13]

    Hikage et al., Cosmology from cosmic shear power spectra with Subaru Hyper Suprime-Cam first-year data, Publ

    C. Hikage et al., Cosmology from cosmic shear power spectra with Subaru Hyper Suprime-Cam first-year data, Publ. Astron. Soc. Jpn. 71, 43 (2019), arXiv:1809.09148 [astro-ph.CO]

    2019 arXiv

  6. [14]

    Hildebrandt et al., KiDS+VIKING-450: Cosmic shear tomography with optical and infrared data, Astron

    H. Hildebrandt et al., KiDS+VIKING-450: Cosmic shear tomography with optical and infrared data, Astron. Astrophys. 633, A69 (2020), arXiv:1812.06076 [astro-ph.CO]

    2020 arXiv

  7. [15]

    Asgari et al., KiDS-1000 cosmology: Cosmic shear constraints and comparison between two point statistics, Astron

    M. Asgari et al., KiDS-1000 cosmology: Cosmic shear constraints and comparison between two point statistics, Astron. Astrophys. 645, A104 (2021), arXiv:2007.15633 [astro-ph.CO]

    2021 arXiv

  8. [16]

    Amon et al

    A. Amon et al. (DES Collaboration), Dark energy survey year 3 results: Cosmology from cosmic shear and robustness to data calibration, Phys. Rev. D 105, 023514 (2022)

    2022

  9. [17]

    Caldwell, A phantom menace? cosmological consequences of a dark energy component with super-negative equation of state, Phys

    R. Caldwell, A phantom menace? cosmological consequences of a dark energy component with super-negative equation of state, Phys. Lett. B 545, 23 (2002). 13

    2002

  10. [18]

    Kamenshchik, U

    A. Kamenshchik, U. Moschella, and V. Pasquier, An alternative to quintessence, Phys. Lett. B 511, 265 (2001)

    2001

  11. [19]

    Nojiri and S

    S. Nojiri and S. D. Odintsov, Modified gravity with negative and positive powers of curvature: Unification of inflation and cosmic acceleration, Phys. Rev. D 68, 123512 (2003)

    2003

  12. [20]

    G. R. Dvali, G. Gabadadze, and M. Porrati, 4-D gravity on a brane in 5-D Minkowski space, Phys. Lett. B 485, 208 (2000), arXiv:hep-th/0005016

    2000 arXiv

  13. [21]

    Eckart, The thermodynamics of irreversible processes

    C. Eckart, The thermodynamics of irreversible processes. iii. relativistic theory of the simple fluid, Phys. Rev. 58, 919 (1940)

    1940

  14. [22]

    Di Prisco, L

    A. Di Prisco, L. Herrera, and J. Ib´ a˜ nez, Qualitative analysis of dissipative cosmologies, Phys. Rev. D63, 023501 (2000)

    2000

  15. [23]

    Zimdahl, D

    W. Zimdahl, D. J. Schwarz, A. B. Balakin, and D. Pav´ on, Cosmic antifriction and accelerated expansion, Phys. Rev. D 64, 063501 (2001)

    2001

  16. [24]

    Velten and D

    H. Velten and D. J. Schwarz, Dissipation of dark matter, Phys. Rev. D 86, 083501 (2012)

    2012

  17. [25]

    Ren and X.-H

    J. Ren and X.-H. Meng, Cosmological model with viscosity media (dark fluid) described by an effective equation of state, Phys. Lett. B 633, 1 (2006)

    2006

  18. [26]

    Xin-He and D

    M. Xin-He and D. Xu, Friedmann cosmology with bulk viscosity: A concrete model for dark energy, Commun. Theor. Phys. 52, 377 (2009)

    2009

  19. [27]

    Colistete, J

    R. Colistete, J. C. Fabris, J. Tossa, and W. Zimdahl, Bulk viscous cosmology, Phys. Rev. D 76, 103516 (2007)

    2007

  20. [28]

    G. S. Khadekar, S. Ray, and X. H. Meng, FLR W viscous cosmological models, arXiv e-prints , arXiv:1611.01023 (2016), arXiv:1611.01023 [physics.gen-ph]

    2016 arXiv

  21. [29]

    A. A. Costa, R. C. G. Landim, B. Wang, and E. Abdalla, Interacting dark energy: possible explanation for 21-cm absorption at cosmic dawn, Eur. Phys. J. C 78, 746 (2018)

    2018

  22. [30]

    Wang and G.-B

    Y. Wang and G.-B. Zhao, Constraining the dark matter vacuum energy interaction using the edges 21 cm absorption signal, Astrophys. J. 869, 26 (2018)

    2018

  23. [31]

    Halder and M

    A. Halder and M. Pandey, Probing the effects of primordial black holes on 21-cm EDGES signal along with interacting dark energy and dark matter–baryon scattering, Mon. Not. Roy. Astron. Soc.508, 3446 (2021), arXiv:2101.05228 [astro-ph.CO]

    2021 arXiv

  24. [32]

    Halder, S

    A. Halder, S. S. Pandey, and A. S. Majumdar, Global 21-cm brightness temperature in viscous dark energy models, JCAP 10, 049, arXiv:2207.09177 [astro-ph.CO]

    arXiv

  25. [33]

    Sahni, A

    V. Sahni, A. Shafieloo, and A. A. Starobinsky, Two new diagnostics of dark energy, Phys. Rev. D 78, 103502 (2008), arXiv:0807.3548 [astro-ph]

    2008 arXiv

  26. [34]

    C. Li, X. Ren, M. Khurshudyan, and Y.-F. Cai, Implications of the possible 21-cm line excess at cosmic dawn on dynamics of interacting dark energy, Phys. Lett. B 801, 135141 (2020)

    2020

  27. [35]

    Z.-K. Guo, N. Ohta, and S. Tsujikawa, Probing the coupling between dark components of the universe, Phys. Rev. D 76, 023508 (2007)

    2007

  28. [36]

    Di Valentino, A

    E. Di Valentino, A. Melchiorri, O. Mena, and S. Vagnozzi, Nonminimal dark sector physics and cosmological tensions, Phys. Rev. D 101, 063502 (2020)

    2020

  29. [37]

    A. A. Costa, X.-D. Xu, B. Wang, and E. Abdalla, Constraints on interacting dark energy models from planck 2015 and redshift-space distortion data, JCAP 2017 (01), 028

    2015

  30. [38]

    Bertolami, F

    O. Bertolami, F. Gil Pedro, and M. Le Delliou, Dark energy–dark matter interaction and putative violation of the equiv- alence principle from the abell cluster a586, Phys. Lett. B 654, 165 (2007)

    2007

  31. [39]

    J.-H. He, B. Wang, and E. Abdalla, Testing the interaction between dark energy and dark matter via the latest observations, Phys. Rev. D 83, 063515 (2011)

    2011

  32. [40]

    Santos, W

    L. Santos, W. Zhao, E. G. M. Ferreira, and J. Quintin, Constraining interacting dark energy with cmb and bao future surveys, Phys. Rev. D 96, 103529 (2017)

    2017

  33. [41]

    W. Yang, S. Pan, and A. Paliathanasis, Cosmological constraints on an exponential interaction in the dark sector, Mon. Not. Roy. Astron. Soc. 482, 1007 (2018)

    2018

  34. [42]

    Le Delliou, R

    M. Le Delliou, R. J. F. Marcondes, and G. B. Lima Neto, New observational constraints on interacting dark energy using galaxy clusters virial equilibrium states, Mon. Not. Roy. Astron. Soc. 490, 1944 (2019)

    2019

  35. [43]

    Gavela, D

    M. Gavela, D. Hern´ andez, L. L. Honorez, O. Mena, and S. Rigolin, Dark coupling, JCAP 2009 (07), 034

    2009

  36. [44]

    J.-H. He, B. Wang, and E. Abdalla, Stability of the curvature perturbation in dark sectors’ mutual interacting models, Phys. Lett. B 671, 139 (2009)

    2009

  37. [45]

    Visser, Jerk, snap, and the cosmological equation of state, Class

    M. Visser, Jerk, snap, and the cosmological equation of state, Class. Quantum Grav. 21 (2003)

    2003

  38. [46]

    D. Adak, D. Majumdar, and S. Pal, Generalizing thawing dark energy models: the standard vis-` a-vis model independent diagnostics, Mon. Not. Roy. Astron. Soc. 437, 831 (2013)

    2013

  39. [47]

    Shafieloo, V

    A. Shafieloo, V. Sahni, and A. A. Starobinsky, New null diagnostic customized for reconstructing the properties of dark energy from baryon acoustic oscillations data, Phys. Rev. D 86, 103527 (2012)

    2012

  40. [48]

    Blake et al., The WiggleZ Dark Energy Survey: mapping the distance–redshift relation with baryon acoustic oscillations, Mon

    C. Blake et al., The WiggleZ Dark Energy Survey: mapping the distance–redshift relation with baryon acoustic oscillations, Mon. Not. Roy. Astron. Soc. 418, 1707 (2011)

    2011

  41. [49]

    A. G. S´ anchezet al., The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological implications of the large-scale two-point correlation function, Mon. Not. Roy. Astron. Soc. 425, 415 (2012)

    2012

  42. [50]

    Haario, M

    H. Haario, M. Laine, A. Mira, and E. Saksman, Dram: Efficient adaptive mcmc, Stat. Comput. 16, 339 (2006)

    2006

  43. [51]

    Haario, E

    H. Haario, E. Saksman, and J. Tamminen, An adaptive metropolis algorithm, Bernoulli 7, 223 (2001)

    2001

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.