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arxiv: 2605.20214 · v1 · pith:IXJGBK4Xnew · submitted 2026-05-05 · ⚛️ physics.gen-ph

Observational Constraints and Cosmological Dynamics of Interacting Fractional Holographic Dark Energy in Light of DESI DR2

Qihong Huang , Hao Chen , Qihong Wu This is my paper

Pith reviewed 2026-05-21 08:31 UTC · model grok-4.3

classification ⚛️ physics.gen-ph
keywords fractional holographic dark energyinteracting dark energyphase space analysiscosmological dynamicsobservational constraintslate-time accelerationDESI DR2
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The pith

Only the interacting fractional holographic dark energy model with combined matter and dark energy terms describes the full cosmic history and drives late-time acceleration.

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

The paper examines three forms of interaction between pressureless matter and fractional holographic dark energy derived from fractional entropy. Fits to data from supernovae, Hubble parameters, baryon acoustic oscillations, and cosmic microwave background favor the interaction forms that include the dark energy density. Phase space analysis shows that only the model with an interaction term proportional to both matter and dark energy densities traces the universe from early matter domination through to a future de Sitter phase. This same model produces the observed late-time acceleration while its statefinder trajectory approaches but does not remain at the standard Lambda cold dark matter fixed point.

Core claim

The central claim is that only the interacting fractional holographic dark energy model with interaction rate Q equal to beta times the Hubble parameter times matter density plus gamma times the Hubble parameter times dark energy density can describe the complete evolutionary history of the universe, as its phase space trajectories converge to the de Sitter fixed point, while also being consistent with current observational constraints and driving the late-time acceleration.

What carries the argument

The interaction term Q = β H ρ_m + γ H ρ_de added to the continuity equations for matter and fractional holographic dark energy.

If this is right

  • The model with the combined interaction term converges to the de Sitter fixed point in the future.
  • Statefinder diagnostics show deviation from Lambda CDM but convergence toward its fixed point.
  • Observational data from SNIa, OHD, BAO, and CMB prefer the interaction forms that include the dark energy density.
  • The model accounts for the transition to observed late-time acceleration.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the fractional entropy origin remains consistent with interactions, similar structures could be tested in other entropy-based dark energy proposals.
  • Higher-precision measurements of the transition redshift to acceleration could tighten bounds on the interaction coefficients.
  • The phase space approach may extend to non-flat cosmologies or models with varying fractional order.

Load-bearing premise

The fractional holographic dark energy density based on fractional entropy keeps its defining form when interaction terms are added to the continuity equations.

What would settle it

A precise measurement of the late-time expansion history or statefinder parameters showing that the universe does not converge to a constant Hubble parameter de Sitter phase would rule out the central claim for this interaction form.

Figures

Figures reproduced from arXiv: 2605.20214 by Hao Chen, Qihong Huang, Qihong Wu.

Figure 1
Figure 1. Figure 1: FIG. 1. Confidence contours for the model parameters of the IFHDE-A model using SNIa, OHD, [PITH_FULL_IMAGE:figures/full_fig_p013_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Confidence contours for the model parameters of the IFHDE-B model using SNIa, OHD, [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Confidence contours for the model parameters of the IFHDE-C model using SNIa, OHD, [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Phase space trajectories. The left panel is plotted for IFHDE-B with the best-fit values, [PITH_FULL_IMAGE:figures/full_fig_p019_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Statefinder diagnostics [PITH_FULL_IMAGE:figures/full_fig_p020_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Cosmological evolution and stability of the IFHDE-C model with the best-fit values. [PITH_FULL_IMAGE:figures/full_fig_p022_6.png] view at source ↗
read the original abstract

Based on the fractional entropy originating from fractional quantum mechanics, the fractional holographic dark energy (FHDE) model has been proposed. In this paper, we consider an interaction between the pressureless matter and FHDE and analyze three different interacting FHDE models. Combining the latest observational data including SNIa, OHD, BAO, and CMB, we estimate the model parameters and find that the interaction forms $Q=\gamma H \rho_{de}$ and $Q=\beta H \rho_{m}+\gamma H \rho_{de}$ show some preference from the observational data. Using phase space analysis, we further find that only interacting FHDE model with $Q=\beta H \rho_{m}+\gamma H \rho_{de}$ can describe the full evolutionary history of the universe. The statefinder diagnostic pair reveals that this model deviates from the $\Lambda$CDM model but converges to the $\Lambda$CDM fixed point and the de Sitter expansion fixed point in the future. Finally, we analyze the evolution of cosmological parameters and demonstrate that this model can drive the late time acceleration of the universe.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript examines three interacting fractional holographic dark energy (FHDE) models with different forms of the interaction term Q between pressureless matter and FHDE. Parameter constraints are obtained from combined SNIa, OHD, BAO, and CMB datasets including DESI DR2; two interaction forms show statistical preference. Phase-space analysis of the autonomous system is then used to argue that only the model with Q = β H ρ_m + γ H ρ_de reproduces the full cosmic evolutionary history, converges to a de Sitter attractor, and drives late-time acceleration, as further supported by statefinder diagnostics.

Significance. If the central modeling assumptions hold, the work supplies timely observational bounds on interacting FHDE using DESI DR2 and integrates dynamical-systems methods to discriminate among interaction forms. Explicit credit is due for the multi-probe likelihood analysis and the attempt to link observational fits to global phase-space behavior.

major comments (2)
  1. [Section 2 and Section 3] Section 2 (model definition): the FHDE energy density is obtained from the fractional entropy expression (Eq. (8) or equivalent) in the non-interacting case. In Section 3 the continuity equations are modified by the addition of Q while the identical functional form of ρ_de is retained without re-derivation or explicit justification under the altered energy transfer. Because the autonomous system, fixed-point locations, and stability conclusions in Section 4 are constructed directly from this ρ_de, the assumption is load-bearing for the claim that only one interaction form works.
  2. [Section 4.2] Section 4.2 (phase-space analysis): the reported convergence to the de Sitter fixed point and the statement that only the Q = β H ρ_m + γ H ρ_de model describes the full history rely on the best-fit values of β and γ obtained from the same observational data used for model selection. No propagation of the posterior uncertainties on β and γ into the locations or eigenvalues of the fixed points is shown, weakening the robustness of the dynamical conclusions.
minor comments (2)
  1. [Table 2] Table 2: the reported ΔAIC and ΔBIC values for the three models should be accompanied by the absolute χ² values and the number of degrees of freedom to allow direct assessment of fit quality.
  2. [Figure 5] Figure 5 (statefinder trajectories): the plot would be clearer if the ΛCDM fixed point and the future de Sitter attractor were explicitly marked with distinct symbols rather than inferred from the curve endpoints.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment below and have revised the manuscript to strengthen the presentation and robustness of the results.

read point-by-point responses

  1. Referee: [Section 2 and Section 3] Section 2 (model definition): the FHDE energy density is obtained from the fractional entropy expression (Eq. (8) or equivalent) in the non-interacting case. In Section 3 the continuity equations are modified by the addition of Q while the identical functional form of ρ_de is retained without re-derivation or explicit justification under the altered energy transfer. Because the autonomous system, fixed-point locations, and stability conclusions in Section 4 are constructed directly from this ρ_de, the assumption is load-bearing for the claim that only one interaction form works.

    Authors: We acknowledge the referee's point that the functional form of ρ_de originates from the fractional entropy in the non-interacting derivation. In the interacting models, we have followed the standard phenomenological approach in the interacting dark energy literature by retaining the same ρ_de expression while adding the interaction term Q to the continuity equations. This assumes the holographic relation is intrinsic to the dark energy component and is not directly altered by the energy transfer. To address the concern, we will add an explicit justification paragraph in the revised Section 3 explaining this assumption and its consistency with the fractional entropy framework. revision: yes

  2. Referee: [Section 4.2] Section 4.2 (phase-space analysis): the reported convergence to the de Sitter fixed point and the statement that only the Q = β H ρ_m + γ H ρ_de model describes the full history rely on the best-fit values of β and γ obtained from the same observational data used for model selection. No propagation of the posterior uncertainties on β and γ into the locations or eigenvalues of the fixed points is shown, weakening the robustness of the dynamical conclusions.

    Authors: We agree that using only the best-fit values without propagating uncertainties reduces the robustness of the dynamical conclusions. In the revised manuscript, we will include additional analysis evaluating the fixed-point locations and eigenvalues at the boundaries of the 1σ and 2σ posterior intervals for β and γ. This will confirm that the qualitative results, including convergence to the de Sitter attractor for the Q = β H ρ_m + γ H ρ_de model, remain consistent within the observationally allowed ranges. revision: yes

Circularity Check

1 steps flagged

FHDE density formula from fractional entropy used unchanged after adding interaction Q, without re-derivation

specific steps
  1. ansatz smuggled in via citation [Abstract and model introduction]
    "Based on the fractional entropy originating from fractional quantum mechanics, the fractional holographic dark energy (FHDE) model has been proposed. In this paper, we consider an interaction between the pressureless matter and FHDE and analyze three different interacting FHDE models."

    The ρ_de expression is taken unchanged from the fractional-entropy definition and substituted into the modified continuity equations that now include Q. The subsequent autonomous system, fixed-point analysis, and conclusion that only the β+γ interaction form describes the full evolutionary history therefore rest on the original ansatz rather than a re-derived density consistent with energy transfer.

full rationale

The paper defines the FHDE density via fractional entropy (from prior proposal), then directly inserts interaction terms Q into the continuity equations while retaining the identical ρ_de functional form. Phase-space analysis and the claim that only Q=βHρ_m + γHρ_de reaches the full history and de Sitter attractor therefore depend on this unadjusted density; altering the dynamics via interaction would in principle require re-deriving ρ_de(H) and could shift fixed-point locations and stability. Observational fitting of β, γ to the same SNIa/OHD/BAO/CMB data then reinforces model preference, but the core load-bearing step is the preserved ansatz rather than a fresh derivation. This produces partial circularity (score 6) without reducing the entire result to a pure fit or self-citation chain.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of the fractional holographic cutoff and the chosen interaction forms. No new particles or forces are postulated beyond the standard dark energy and matter sectors.

free parameters (2)
  • fractional parameter
    The order of the fractional derivative or entropy that defines the holographic density; fitted or chosen to match observations.
  • interaction parameters β and γ
    Dimensionless coupling constants in the energy transfer rate Q; directly fitted to SNIa, BAO, CMB data.
axioms (2)
  • domain assumption The universe is described by a flat FLRW metric with standard continuity equations modified by an interaction term.
    Invoked when writing the Friedmann and continuity equations for the interacting components.
  • domain assumption Fractional holographic dark energy density follows from fractional entropy in the same way as standard holographic dark energy follows from Bekenstein entropy.
    Stated in the model construction section as the starting point for FHDE.

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Works this paper leans on

108 extracted references · 108 canonical work pages

  1. [1]

    By differentiating Equation (10), the statefinder parametersrandsare expressed in terms of Ω′ m and Ω′ de

    ,(33) whereHis the Hubble parameter, andqis the deceleration parameter defined in Equa- tion (11). By differentiating Equation (10), the statefinder parametersrandsare expressed in terms of Ω′ m and Ω′ de. The evolution curves of the universe in ther−sandr−qparameter space are then obtained through numerical solution of Equations (13) and (14). In the lef...

    work page

  2. [2]

    Measurements of Ω and Λ from 42 High-Redshift Supernovae.Astrophys

    Perlmutter, S.; Aldering, G.; Goldhaber, G.; Knop, R.; Nugent, P.; Castro, P.; Deustua, S.; Fabbro, S.; Goobar, A.; Groom, D.; et al. Measurements of Ω and Λ from 42 High-Redshift Supernovae.Astrophys. J.1999,517, 565–586

    work page 1999

  3. [3]

    Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant.Astron

    Riess, A.; Filippenko, A.; Challis, P.; Clocchiattia, A.; Diercks, A.; Garnavich, P.; Gilliland, 23 R.; Hogan, C.; Jha, S.; Kirshner, R.; et al. Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant.Astron. J.1998,116, 1009–1038

    work page 1998

  4. [4]

    First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters.Astrophys

    Spergel, D.; Verde, L.; Peiris, H.; Komatsu, E.; Nolta, M.; Bennett, C.; Halpern, M.; Hinshaw, G.; Jarosik, N.; Kogut, A.; et al. First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters.Astrophys. J. Suppl.2003,148, 175–194

    work page 2003

  5. [5]

    Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology.Astrophys

    Spergel, D.; Bean, R.; Dore, O.; Nolta, M.; Bennett, C.; Dunkley, J.; Hinshaw, G.; Jarosik, N.; Komatsu, E.; Page, L.; et al. Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology.Astrophys. J. Suppl.2007,170, 377

    work page 2007

  6. [6]

    Cosmological parameters from SDSS and WMAP.Phys

    Tegmark, M.; Strauss, M.; Blanton, M.; Abazajian, K.; Dodelson, S.; Sandvik, H.; Wang, X.; Weinberg, D.; Zehavi, I.; Bahcall, N.; et al. Cosmological parameters from SDSS and WMAP.Phys. Rev. D2004,69, 103501

    work page

  7. [7]

    Detection of the baryon acoustic peak in the large-scale correlation function of SDSS luminous red galaxies.Astron

    Eisenstein, D.; Zehavi, I.; Hogg, D.; Scoccimarro, R.; Blanton, M.; Nichol, R.; Scranton, R.; Seo, H.; Tegmark, M.; Zheng, Z.; et al. Detection of the baryon acoustic peak in the large-scale correlation function of SDSS luminous red galaxies.Astron. J.2005,633, 560–574

    work page 2005

  8. [8]

    The Cosmological Constant and Dark Energy.Rev

    Peebles, P.; Ratra, B. The Cosmological Constant and Dark Energy.Rev. Mod. Phys.2003, 75, 559

    work page 2003

  9. [9]

    Aghanim, N. et al. [Planck Collaboration] Planck 2018 results VI. Cosmological parameters. Astron. Astrophys.2020,641, A6

    work page 2018

  10. [10]

    The cosmological constant problem.Rev

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

    work page 1989

  11. [11]

    Cosmological tracking solutions.Phys

    Steinhardt, P.; Wang, L.; Zlatev, I. Cosmological tracking solutions.Phys. Rev. D1999,59, 123504

    work page

  12. [12]

    Cosmology and the fate of dilatation symmetry.Nucl

    Wetterich, C. Cosmology and the fate of dilatation symmetry.Nucl. Phys. B1988,302, 668–696

    work page

  13. [13]

    Cosmological consequences of a rolling homogeneous scalar field.Phys

    Ratra, B.; Peebles, P. Cosmological consequences of a rolling homogeneous scalar field.Phys. Rev. D1988,37, 3406–3427

    work page

  14. [14]

    Cosmological Imprint of an Energy Component with General Equation of State.Phys

    Caldwell, R.; Dave, R.; Steinhardt, P. Cosmological Imprint of an Energy Component with General Equation of State.Phys. Rev. Lett.1998,80, 1582–1585. 24

    work page 1998

  15. [15]

    Dark energy constraints from the cosmic age and supernova

    Feng, B.; Wang, X.; Zhang, X. Dark energy constraints from the cosmic age and supernova. Phys. Lett. B2005,607, 35–41

    work page

  16. [16]

    Oscillating quintom and the recurrent universe.Phys

    Feng, B.; Li, M.; Piao, Y.; Zhang, X. Oscillating quintom and the recurrent universe.Phys. Lett. B2006,634, 101–105

    work page

  17. [17]

    Cosmological evolution of a quintom model of dark energy.Phys

    Guo, Z.; Piao, Y.; Zhang, X.; Zhang, Y. Cosmological evolution of a quintom model of dark energy.Phys. Lett. B2005,608, 177–182

    work page

  18. [18]

    A phantom menace? Cosmological consequences of a dark energy component with super-negative equation of state.Phys

    Caldwell, R. A phantom menace? Cosmological consequences of a dark energy component with super-negative equation of state.Phys. Lett. B2002,545, 23–29

    work page

  19. [19]

    Phantom Energy: Dark Energy withω <−1 Causes a Cosmic Doomsday.Phys

    Caldwell, R.; Kamionkowski, M.; Weinberg, N. Phantom Energy: Dark Energy withω <−1 Causes a Cosmic Doomsday.Phys. Rev. Lett.2003,91, 071301

    work page 2003

  20. [20]

    Kinetically driven quintessence.Phys

    Chiba, T.; Okabe, T.; Yamaguchi, M. Kinetically driven quintessence.Phys. Rev. D2000, 62, 023511

    work page

  21. [21]

    Essentials of k-essence.Phys

    Armendariz-Picon, C.; Mukhanov, V.; Steinhardt, P. Essentials of k-essence.Phys. Rev. D 2001,63, 103510

    work page 2001

  22. [22]

    Statefinder diagnostic andω−ω ′ analysis for the agegraphic dark energy models without and with interaction.Phys

    Wei, H.; Cai, R. Statefinder diagnostic andω−ω ′ analysis for the agegraphic dark energy models without and with interaction.Phys. Lett. B2007,655, 1–6

    work page

  23. [23]

    A new model of agegraphic dark energy.Phys

    Wei, H.; Cai, R. A new model of agegraphic dark energy.Phys. Lett. B2008,660, 113–117

    work page

  24. [24]

    A dark energy model characterized by the age of the Universe.Phys

    Cai, R. A dark energy model characterized by the age of the Universe.Phys. Lett. B2007, 657, 228–231

    work page

  25. [25]

    Effective Field Theory, Black Holes, and the Cosmological Constant.Phys

    Cohen, A.; Kaplan, D.; Nelson, A. Effective Field Theory, Black Holes, and the Cosmological Constant.Phys. Rev. Lett.1999,82, 4971–4974

    work page 1999

  26. [26]

    Entropy bounds and dark energy.Phys

    Hsu, S. Entropy bounds and dark energy.Phys. Lett. B2004,594, 13–16

    work page

  27. [27]

    Holography and a variable cosmological constant.Phys

    Horvat, R. Holography and a variable cosmological constant.Phys. Rev. D2004,70, 087301

    work page

  28. [28]

    A model of holographic dark energy.Phys

    Li, M. A model of holographic dark energy.Phys. Lett. B2004,603, 1–5

    work page

  29. [29]

    Holographic dark energy.Phys

    Wang, S.; Wang, Y.; Li, M. Holographic dark energy.Phys. Rep.2017,696, 1–57

    work page 2017

  30. [30]

    Anti de Sitter space and holography.Adv

    Witten, E. Anti de Sitter space and holography.Adv. Theor. Math. Phys.1998,2, 253–291

    work page 1998

  31. [31]

    The holographic principle.Rev

    Bousso, R. The holographic principle.Rev. Mod. Phys.2002,74, 825

    work page 2002

  32. [32]

    Tsallis holographic dark energy.Phys

    Tavayef, M.; Sheykhi, A.; Bamba, K.; Moradpour, H. Tsallis holographic dark energy.Phys. 25 Lett. B2018,781, 195–200

    work page

  33. [33]

    Barrow holographic dark energy.Phys

    Saridakis, E. Barrow holographic dark energy.Phys. Rev. D2020,102, 123525

    work page

  34. [34]

    Prospecting black hole thermodynamics with fractional quantum mechanics.Eur

    Jalalzadeh, S.; da Silva, F.; Moniz, P. Prospecting black hole thermodynamics with fractional quantum mechanics.Eur. Phys. J. C2021,81, 632

    work page

  35. [35]

    Fractional holographic dark energy.Phys

    Trivedi, O.; Bidlan, A.; Moniz, P. Fractional holographic dark energy.Phys. Lett. B2024, 858, 139074

    work page

  36. [36]

    Stability analysis of a Tsallis holographic dark energy model.Class

    Huang, Q.; Huang, H.; Chen, J.; Zhang, L.; Tu, F. Stability analysis of a Tsallis holographic dark energy model.Class. Quantum Grav.2019,36, 175001

    work page 2019

  37. [37]

    Dynamical analysis and statefinder of Barrow holographic dark energy.Eur

    Huang, Q.; Huang, H.; Xu, B.; Tu, F.; Chen, J. Dynamical analysis and statefinder of Barrow holographic dark energy.Eur. Phys. J. C2021,81, 686

    work page

  38. [38]

    A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s −1 Mpc−1 Uncertainty from the Hubble Space Telescope and the SH0ES Team.Astrophys

    Riess, A.; Yuan, W.; Macri, L.; Scolnic, D.; Brout, D.; Casertano, S.; Jones, D.; Murakami, Y.; Breuval, L.; Brink, T.; et al. A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s −1 Mpc−1 Uncertainty from the Hubble Space Telescope and the SH0ES Team.Astrophys. J. Lett.2022,934, L7

    work page 2022

  39. [39]

    The Pantheon+ Analysis: Cosmological Constraints.Astrophys

    Brout, D.; Scolnic, D.; Popovic, B.; Riess, A.; Zuntz, J.; Kessler, R.; Carr, A.; Davis, T.; Hinton, S.; Jones, D.; et al. The Pantheon+ Analysis: Cosmological Constraints.Astrophys. J.2022,938, 110

    work page 2022

  40. [40]

    The Pantheon+ Analysis: The Full Data Set and Light-curve Release.Astrophys

    Scolnic, D.; Brout, D.; Carr, A.; Riess, A.; Davis, T.; Dwomoh, A.; Jones, D.; Ali, N.; Charvu, P.; Chen, R.; et al. The Pantheon+ Analysis: The Full Data Set and Light-curve Release.Astrophys. J.2022,938, 113

    work page 2022

  41. [41]

    Using lower-redshift, non-CMB, data to constrain the Hubble constant and other cosmological parameters.Mon

    Cao, S.; Ratra, B. Using lower-redshift, non-CMB, data to constrain the Hubble constant and other cosmological parameters.Mon. Not. R. Astron. Soc.2022,513, 5686–5700

    work page 2022

  42. [42]

    Abdul Karim, M. et al. [DESI Collaboration] DESI DR2 results. II. Measurements of baryon acoustic oscillations and cosmological constraints.Phys. Rev. D2025,112, 083515

    work page

  43. [43]

    Updated observational constraints on interacting holographic dark energy models in a non-flat universe.Eur

    Shen, X.; Xu, B.; Zhang, K.; Fu,X.; Huang, Q.; Ren, L.; Zhang, Z. Updated observational constraints on interacting holographic dark energy models in a non-flat universe.Eur. Phys. J. C2026,86, 406

    work page

  44. [44]

    Photon rest mass from localized fast radio bursts with an 26 improved distribution of the dispersion measure from extragalactic gas.Phys

    Zhang, Y.; Liu, Y.; Yu, H.; Wu, P. Photon rest mass from localized fast radio bursts with an 26 improved distribution of the dispersion measure from extragalactic gas.Phys. Rev. D2026, 113, 043513

    work page

  45. [45]

    Agegraphic Dark Energy from Entropy of the Anti-de Sitter Black Hole.Universe2025,11, 336

    Huang, Q.; Liu, Y.; Huang, H. Agegraphic Dark Energy from Entropy of the Anti-de Sitter Black Hole.Universe2025,11, 336

    work page

  46. [46]

    Cosmological-model-independent determination of Hubble constant from fast radio bursts and Hubble parameter measurements.Astrophys

    Liu, Y.; Yu, H.; Wu, P. Cosmological-model-independent determination of Hubble constant from fast radio bursts and Hubble parameter measurements.Astrophys. J. Lett.2023,946, L49

    work page 2023

  47. [47]

    Zhang, Z

    Shen, X.; Xu, B.; Zhang, K.; Fu, X.; Ren, L. Zhang, Z. Revisiting the constraints on interact- ing holographic dark energy models with current observational data.Eur. Phys. J. C2025, 85, 992

    work page

  48. [48]

    Revisiting cosmic acceleration with DESI BAO.Eur

    Wang, J.; Yu, H.; Wu, P. Revisiting cosmic acceleration with DESI BAO.Eur. Phys. J. C 2025,85, 853

    work page 2025

  49. [49]

    Alleviating the Hubble-constant tension and the growth tension via a transition of absolute magnitude favored by the Pantheon+ sample.Phys

    Liu, Y.; Yu, H.; Wu, P. Alleviating the Hubble-constant tension and the growth tension via a transition of absolute magnitude favored by the Pantheon+ sample.Phys. Rev. D2024, 110, L021304

    work page

  50. [50]

    Probing cosmic background dynamics with a cosmological- model-independent method.Mon

    Liu, Y.; Wang, B.; Yu, H.; Wu, P. Probing cosmic background dynamics with a cosmological- model-independent method.Mon. Not. R. Astron. Soc.2024,533, 244

    work page 2024

  51. [51]

    Revisiting kink-like parametrization and constraints using OHD/Pantheon+/BAO samples.Phys

    Arora, S.; Sahoo, P. Revisiting kink-like parametrization and constraints using OHD/Pantheon+/BAO samples.Phys. Dark Universe2024,45, 101510

    work page

  52. [52]

    Cosmological dynamics and observational constraints on a viable f(Q) nonmetric gravity model.Int

    Oliveros, A.; Acero, M. Cosmological dynamics and observational constraints on a viable f(Q) nonmetric gravity model.Int. J. Mod. Phys. D2024,33, 2450004

    work page

  53. [53]

    Observational constraints on a logarithmic scalar field dark energy model and black hole mass evolution in the Universe

    Wang, D.; Koussour, M.; Malik, A.; Myrzakulov, N.; Mustafa, G. Observational constraints on a logarithmic scalar field dark energy model and black hole mass evolution in the Universe. Eur. Phys. J. C2023,83, 670

    work page

  54. [54]

    Revisiting a non-parametric reconstruction of the deceleration parameter from combined background and the growth rate data.Phys

    Mukherjee, P.; Banerjee, N. Revisiting a non-parametric reconstruction of the deceleration parameter from combined background and the growth rate data.Phys. Dark Universe2022, 36, 100998

    work page

  55. [55]

    Constraining the curvature density parameter in cosmology

    Mukherjee, P.; Banerjee, N. Constraining the curvature density parameter in cosmology. 27 Phys. Rev. D2022,105, 063516

    work page

  56. [56]

    Using Pantheon and DES supernova, baryon acoustic oscillation, and Hubble parameter data to constrain the Hubble constant, dark energy dynamics, and spatial curvature.Mon

    Cao, S.; Ryan, J.; Ratra, B. Using Pantheon and DES supernova, baryon acoustic oscillation, and Hubble parameter data to constrain the Hubble constant, dark energy dynamics, and spatial curvature.Mon. Not. R. Astron. Soc.2021,504, 300

    work page 2021

  57. [57]

    Late-time acceleration with a scalar field source: Observational constraints and statefinder diagnostics.Phys

    Pacif, S.; Arora, S.; Sahoo, P. Late-time acceleration with a scalar field source: Observational constraints and statefinder diagnostics.Phys. Dark Universe2021,32, 100804

    work page

  58. [58]

    Cosmological Constraints on the Coupling Model from Observational Hubble Parameter and Baryon Acoustic Oscillation Measurements

    Cao, S.; Zhang, T.; Wang, X.; and Zhang, T. Cosmological Constraints on the Coupling Model from Observational Hubble Parameter and Baryon Acoustic Oscillation Measurements. Universe2021,7, 57

    work page

  59. [59]

    Graduated dark energy: Observational hints of a spontaneous sign switch in the cosmological constant.Phys

    Akarsu, O.; Barrow, J.; Escamilla, L.; Vazquez, J. Graduated dark energy: Observational hints of a spontaneous sign switch in the cosmological constant.Phys. Rev. D2020,101, 063528

    work page

  60. [60]

    The evidence of cosmic acceleration and observational constraints.J

    Yang, Y.; Gong, Y. The evidence of cosmic acceleration and observational constraints.J. Cosmol. Astropart. Phys.2020,6, 059

    work page 2020

  61. [61]

    Revisit of constraints on dark energy with Hubble parameter measurements including future redshift drift observations.J

    Liu, Y.; Guo, R.; Zhang, J.; Zhang, X. Revisit of constraints on dark energy with Hubble parameter measurements including future redshift drift observations.J. Cosmol. Astropart. Phys.2019,5, 016

    work page 2019

  62. [62]

    Observational constraints on cosmo- logical future singularities.Eur

    Jimenez, J.; Lazkoz, R.; Saez-Gomez, D.; Salzano, V. Observational constraints on cosmo- logical future singularities.Eur. Phys. J. C2016,76, 631

    work page

  63. [63]

    The effect of different observational data on the constraints of cosmological parameters.Mon

    Gong, Y.; Gao, Q.; Zhu, Z. The effect of different observational data on the constraints of cosmological parameters.Mon. Not. R. Astron. Soc.2013,430, 3142–3154

    work page 2013

  64. [64]

    Figure of merit and different combinations of observational data sets

    Su, Q.; Tuo, Z.; Cai, R. Figure of merit and different combinations of observational data sets. Phys. Rev. D2011,84, 103519

    work page

  65. [65]

    Observational constraint on dynamical evolution of dark energy.J

    Gong, Y.; Cai, R.; Chen, Y.; Zhu, Z. Observational constraint on dynamical evolution of dark energy.J. Cosmol. Astropart. Phys.2010,1001, 019

    work page 2010

  66. [66]

    Observational constraints on f(T) theory.Phys

    Wu, P.; Yu, H. Observational constraints on f(T) theory.Phys. Lett. B2010,693, 415–420

    work page

  67. [67]

    Observational constraints on the acceleration of the Universe.Phys

    Gong, Y.; Wang, A. Observational constraints on the acceleration of the Universe.Phys. Rev. D2006,73, 083506. 28

    work page

  68. [68]

    Constraints on a variable dark energy model with recent observations.Phys

    Wu, P.; Yu, H. Constraints on a variable dark energy model with recent observations.Phys. Lett. B2006,643, 315–318

    work page

  69. [69]

    Constraints on spatial curvature and dark energy dynamics in the wCDM model from DESI DR1 and DR2.J

    Yadav, M.; Dixit, A.; Barak, M.; Pradhan, A. Constraints on spatial curvature and dark energy dynamics in the wCDM model from DESI DR1 and DR2.J. High Energy Astrophys. 2026,50, 100514

    work page 2026

  70. [70]

    Cosmological Constraints on the Phenomeno- logical Interacting Dark Energy Model with Fermi Gamma-Ray Bursts and DESI DR2.J

    Zhu, Z.; Jiang, Q.; Liu, Y.; Wu, P.; Liang, N. Cosmological Constraints on the Phenomeno- logical Interacting Dark Energy Model with Fermi Gamma-Ray Bursts and DESI DR2.J. High Energy Astrophys.2026,51, 100377

    work page 2026

  71. [71]

    Probing theH 0 Tension with Holographic Dark Energy in Unimodular Gravity: Insights from DESI DR2.Eur

    Plaza, F.; Leon, G.; Kraiselburd, L. Probing theH 0 Tension with Holographic Dark Energy in Unimodular Gravity: Insights from DESI DR2.Eur. Phys. J. C2025,85, 1262

    work page

  72. [72]

    Dark Degeneracy in DESI DR2: Interacting or Evolving Dark Energy?Phys

    Petri, V.; Marra, V.; Marttens, R. Dark Degeneracy in DESI DR2: Interacting or Evolving Dark Energy?Phys. Rev. D2026,113, 023504

    work page

  73. [73]

    Exploring non-cold dark matter in a scenario of dynamical dark energy with DESI DR2 data.Phys

    Li, T.; Wu, P.; Du, G.; Yao, Y.; Zhang, J.; Zhang, X. Exploring non-cold dark matter in a scenario of dynamical dark energy with DESI DR2 data.Phys. Dark Universe2025,50, 102068

    work page

  74. [74]

    Reconstructing dark energy with model independent methods after DESI DR2 BAO.Eur

    Li, J.; Wang, S. Reconstructing dark energy with model independent methods after DESI DR2 BAO.Eur. Phys. J. C2025,85, 1308

    work page

  75. [75]

    Cosmic sign-reversal: Non-parametric reconstruction of interacting dark energy with DESI DR2.J

    Li, Y.; Zhang, X. Cosmic sign-reversal: Non-parametric reconstruction of interacting dark energy with DESI DR2.J. Cosmol. Astropart. Phys.2025,12, 018

    work page 2025

  76. [76]

    Revisiting the phenomenologically emergent dark energy model: Is non-zero equation of state of dark matter favored by DESI DR2?J

    Li, T.; Zhang, Y.; Yao, Y.; Wu, P.; Zhang, J.; Zhang, X. Revisiting the phenomenologically emergent dark energy model: Is non-zero equation of state of dark matter favored by DESI DR2?J. Cosmol. Astropart. Phys.2025,12, 048

    work page 2025

  77. [77]

    Constraints on Barrow and Tsallis Holographic Dark Energy from DESI DR2 BAO data.JHEAp2026,49, 100427

    Luciano, G.; Paliathanasis, A.; Saridakis, E. Constraints on Barrow and Tsallis Holographic Dark Energy from DESI DR2 BAO data.JHEAp2026,49, 100427

    work page

  78. [78]

    Model-Independent Dark Energy Measurements from DESI DR2 and Planck 2015 Data

    Wang, Y.; Freese, K. Model-Independent Dark Energy Measurements from DESI DR2 and Planck 2015 Data. Model-Independent Dark Energy Measurements from DESI DR2 and Planck 2015 Data.J. Cosmol. Astropart. Phys.2026,02, 023

    work page 2015

  79. [79]

    Revisiting the Hubble tension problem in the framework of holographic dark 29 energy.Mon

    Li, J.; Wang, S. Revisiting the Hubble tension problem in the framework of holographic dark 29 energy.Mon. Not. R. Astron. Soc.2026,548, 584

    work page 2026

  80. [80]

    New constraints on interacting dark energy from DESI DR2 BAO observations.Phys

    Silva, E.; Sabogal, M.; Scherer, M.; Nunes, R.; Valentino, E.; Kumar, S. New constraints on interacting dark energy from DESI DR2 BAO observations.Phys. Rev. D2025,111, 123511

    work page

Showing first 80 references.