arxiv: 2511.21789 · v2 · submitted 2025-11-26 · 🌌 astro-ph.CO · hep-th

Cosmological Constraints on 4D Einstein-Gauss-Bonnet Gravity and Kaniadakis Holographic Dark Energy: Implications for Black Hole Shadows

Xiang-Qian Li , Hao-Peng Yan , Xiao-Jun Yue This is my paper

Pith reviewed 2026-05-17 04:44 UTC · model grok-4.3

classification 🌌 astro-ph.CO hep-th

keywords Einstein-Gauss-Bonnet gravityKaniadakis holographic dark energyblack hole shadowscosmological constraintsdark energy modelsEvent Horizon Telescopephantom equation of state

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The pith

Black hole shadows retain a roughly 6 percent intrinsic deviation from LambdaCDM at redshift 2 in 4D Einstein-Gauss-Bonnet gravity with Kaniadakis holographic dark energy.

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

The paper examines the cosmological evolution of black hole shadows within 4D Einstein-Gauss-Bonnet gravity coupled to Kaniadakis holographic dark energy, taking the future event horizon as the infrared cutoff. Markov Chain Monte Carlo constraints from cosmic chronometers, Pantheon+ supernovae, and DESI baryon acoustic oscillations favor a phantom-like equation of state, with parameters consistent with general relativity and standard holographic dark energy at the one-sigma level. When the shadow radius is evolved including accretion and a dispersive plasma medium, environmental effects cause overall shrinkage at high redshift. A residual intrinsic deviation of about 6 percent nevertheless persists at redshift 2 relative to the LambdaCDM prediction under a conservative accretion setup. The results indicate that population analyses of black hole shadows may help isolate subtle dynamical dark energy effects from the standard cosmological model.

Core claim

In the 4D EGB gravity model coupled to KHDE, the best-fit parameters are c approximately 1.18, beta approximately 2.26, and alpha approximately -0.004. Standard holographic cases produce monotonic evolution of black hole mass and vacuum shadow radius, while phantom-divide crossing yields non-monotonic behavior. Inclusion of dispersive plasma leads to refraction-dominated shrinkage of the observable shadow, yet a residual intrinsic deviation of approximately 6 percent for the conservative accretion setup remains at redshift 2 relative to the LambdaCDM prediction.

What carries the argument

The observable black hole shadow radius evolved in a universe whose dark energy density is set by Kaniadakis entropy with the future event horizon as infrared cutoff.

If this is right

Phantom-like dark energy evolution produces non-monotonic changes in black hole mass and shadow radius over cosmic time.
The accretion history of black holes is sensitive to the thermodynamic sector of the dark energy model.
Plasma refraction dominates environmental effects on the shadow but leaves a detectable intrinsic difference at moderate redshifts.
Precision studies of black hole shadow populations can disentangle dynamical dark energy imprints from the standard cosmological paradigm.

Where Pith is reading between the lines

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

Higher-resolution imaging of supermassive black holes at intermediate redshifts could directly test the predicted deviation.
The same shadow-evolution approach could be applied to other holographic dark energy models to search for distinctive signatures.
Confirmation of the deviation would supply an independent probe of dark energy dynamics that complements distance and expansion-rate measurements.

Load-bearing premise

The future event horizon serves as the infrared cutoff for the Kaniadakis holographic dark energy and the accretion history follows a fixed conservative setup whose details are not varied across scenarios.

What would settle it

A population measurement of black hole shadow radii at redshift 2 that agrees with the LambdaCDM prediction to better than 6 percent after subtraction of plasma and accretion effects would rule out the predicted residual intrinsic deviation.

Figures

Figures reproduced from arXiv: 2511.21789 by Hao-Peng Yan, Xiang-Qian Li, Xiao-Jun Yue.

**Figure 2.** Figure 2: The Hubble parameter H(z) as a function of redshift. The blue solid line represents the best-fit KHDE model (H0 = 73.6, c = 0.70, α = 0.146), demonstrating strong agreement with the Cosmic Chronometers data (black dots). back to higher redshifts, the fluid transitions into the quintessence regime (w > −1). The EGB coupling α modulates this trajectory, with positive α suppressing the high-redshift value of … view at source ↗

**Figure 3.** Figure 3: Evolution of the dark energy equation of state [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗

**Figure 4.** Figure 4: Evolution of the normalized black hole mass [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗

**Figure 5.** Figure 5: Evolution of the black hole shadow radius in an optical vacuum ( [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗

**Figure 6.** Figure 6: Impact of Plasma Environment. (a) Comparison of shadow evolution in optical vacuum (k0 = 0) versus dispersive plasma (k0 > 0) for fixed h = 1. (b) Sensitivity to the radial profile slope h for fixed density k0 = 0.2. The baseline model is Bekenstein-Hawking-GR. 2. Frequency Redshift (ω term): Due to the cosmic expansion, the photon frequency ω observed at a high redshift z relates to the observed frequency… view at source ↗

read the original abstract

The direct imaging of black holes by the Event Horizon Telescope (EHT) enables strong-field tests of gravity. We study the cosmological evolution and the black-hole shadow radius in 4D Einstein-Gauss-Bonnet (EGB) gravity coupled to Kaniadakis holographic dark energy (KHDE), adopting the future event horizon as the infrared cutoff. Using Cosmic Chronometers, Pantheon+ Type Ia supernovae, and DESI BAO data, we constrain the model with a Markov Chain Monte Carlo analysis. The best-fit values favor a phantom-like equation of state driven by Kaniadakis entropy ($c\simeq 1.18$, $\beta\simeq 2.26$), but $\beta$ remains weakly constrained ($\beta=2.26^{+0.11}_{-2.20}$), consistent with the standard holographic limit $\beta\to0$ at $1\sigma$. The EGB coupling is constrained to $\alpha\simeq -0.004$, also consistent with General Relativity ($\alpha=0$) at $1\sigma$. Guided by the posterior, we define five representative scenarios to probe the dynamical phase space. We find that the accretion history is highly sensitive to the thermodynamic sector: standard holographic cases yield monotonic evolution, whereas phantom-divide crossing leads to non-monotonic behavior in both the black hole mass and the vacuum shadow radius. Including a dispersive plasma medium, refraction dominates over intrinsic mass growth and induces an overall shrinkage of the observable shadow at high redshift; nevertheless, a residual intrinsic deviation of $\sim6\%$ (for our conservative accretion setup) persists at $z\simeq2$ relative to the $\Lambda$CDM prediction. These results indicate that, despite environmental dominance, precision population analyses of black hole shadows may help disentangle subtle dynamical dark-energy imprints from the standard cosmological paradigm.

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.

Desk Editor's Note private letter to a colleague

This paper runs 4D EGB plus Kaniadakis HDE through MCMC on current data and reports a 6% residual shadow offset at z~2, but that offset sits on one fixed accretion model that is not varied.

read the letter

The main takeaway is that the authors combine two existing extensions—4D Einstein-Gauss-Bonnet gravity and Kaniadakis holographic dark energy—then constrain them with Cosmic Chronometers, Pantheon+ supernovae, and DESI BAO. The fits land close to general relativity, with alpha near zero and beta only weakly bounded, consistent with the standard holographic limit at 1 sigma. They then pick five posterior-guided scenarios and track black-hole mass and shadow radius, showing non-monotonic evolution when the equation of state crosses the phantom divide. Adding a dispersive plasma, refraction shrinks the observable shadow at high redshift, yet a roughly 6% intrinsic offset relative to Lambda CDM survives at z approximately 2 for their chosen setup. That combination of data fit plus shadow calculation is the concrete step they take beyond the cited prior work on each piece separately. The MCMC reporting and consistency checks with GR and standard HDE are straightforward and useful. The soft spot is exactly where the stress-test note flags: the 6% figure is tied to one conservative accretion history whose parameters are held fixed across all five scenarios. No alternative Bondi rates, efficiencies, or plasma relations are tested, so the relative weight of intrinsic growth versus refraction could shift with modest changes in those assumptions. Because the scenarios themselves come from the same posterior, the non-monotonic behavior and the offset are downstream consequences rather than independent forecasts. This work is aimed at people who already follow holographic dark energy or strong-field tests with EHT data. A reader looking for how these models behave under current constraints and a shadow observable will find the numbers and the qualitative trends worth seeing. It is coherent enough on its own terms to deserve a serious referee, mainly to check whether the environmental modeling can be made more robust.

Referee Report

1 major / 2 minor

Summary. The manuscript constrains 4D Einstein-Gauss-Bonnet gravity coupled to Kaniadakis holographic dark energy (with future event horizon as IR cutoff) using Cosmic Chronometers, Pantheon+ supernovae, and DESI BAO data via MCMC. Best-fit values favor phantom-like behavior (c≈1.18, β≈2.26, α≈−0.004), consistent with GR and standard holographic limits at 1σ. Five representative scenarios drawn from the posterior are used to evolve black-hole mass and shadow radius, incorporating accretion and a dispersive plasma medium. The analysis finds that refraction dominates and shrinks the observable shadow at high redshift, yet a residual ∼6% intrinsic deviation from ΛCDM persists at z≃2 for the adopted conservative accretion setup, suggesting that precision shadow population studies could isolate dynamical dark-energy effects.

Significance. If the central modeling assumptions prove robust, the work provides a concrete link between late-time cosmological constraints and strong-field observables, extending EHT shadow measurements to test modified gravity plus holographic dark energy. The MCMC analysis with three independent datasets, explicit consistency checks against GR and β→0 limits, and the identification of non-monotonic mass evolution in phantom-crossing cases constitute clear strengths that enhance reproducibility and falsifiability.

major comments (1)

[Abstract and § on shadow evolution] Abstract and the section describing the five representative scenarios: the headline claim of a residual ∼6% intrinsic shadow deviation at z≃2 (and the consequent suggestion that precision population analyses can disentangle DE imprints) rests on a single fixed conservative accretion setup whose parameters are not varied across the scenarios. The text states that refraction dominates yet an offset remains “for our conservative accretion setup”; because the non-monotonic evolution is itself sensitive to the thermodynamic sector, the absence of any exploration of alternative Bondi rates, efficiencies, or plasma dispersion relations makes the persistence of the 6% offset load-bearing for the central assertion.

minor comments (2)

[Model setup] The definition of the infrared cutoff and the precise form of the Kaniadakis entropy correction could be stated explicitly in the model section to aid reproducibility.
[Figures] Figure captions for the shadow-radius evolution plots should indicate whether the curves include the plasma refraction term or show the vacuum case only.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. We address the major comment point by point below, indicating the revisions we intend to implement.

read point-by-point responses

Referee: [Abstract and § on shadow evolution] Abstract and the section describing the five representative scenarios: the headline claim of a residual ∼6% intrinsic shadow deviation at z≃2 (and the consequent suggestion that precision population analyses can disentangle DE imprints) rests on a single fixed conservative accretion setup whose parameters are not varied across the scenarios. The text states that refraction dominates yet an offset remains “for our conservative accretion setup”; because the non-monotonic evolution is itself sensitive to the thermodynamic sector, the absence of any exploration of alternative Bondi rates, efficiencies, or plasma dispersion relations makes the persistence of the 6% offset load-bearing for the central assertion.

Authors: We appreciate the referee highlighting this aspect of our analysis. The conservative accretion setup (including fixed Bondi rates, efficiencies, and plasma dispersion) was deliberately chosen as a representative baseline drawn from the literature to isolate the effects of the different dark-energy scenarios on black-hole mass and shadow evolution. This allows direct comparison of monotonic versus non-monotonic behaviors arising from the thermodynamic sector of the KHDE model. We agree that the precise numerical value of the residual offset could shift under alternative parameter choices and that a full sensitivity study would strengthen the claim. In the revised manuscript we will (i) qualify the abstract to state explicitly that the ∼6% figure applies to our conservative accretion setup and (ii) add a short paragraph in the shadow-evolution section discussing how variations in Bondi accretion parameters or plasma relations might modulate the offset while noting that refraction remains dominant. These changes will reduce the load-bearing character of the single-setup result without requiring an exhaustive new parameter scan, which lies beyond the present scope. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation uses independent data constraints to explore separate observable implications

full rationale

The paper performs MCMC constraints on parameters (c, β, α) using external cosmological datasets (Cosmic Chronometers, Pantheon+, DESI BAO). Five representative scenarios are then selected from that posterior solely to illustrate dynamical behavior in the black-hole shadow calculation under a fixed accretion model. The reported ~6% residual deviation at z≃2 is a numerical outcome of integrating the constrained cosmology with the chosen accretion and plasma refraction prescriptions; it is not equivalent to any input datum or fit by construction. No self-definitional equations, fitted quantities renamed as predictions, or load-bearing self-citations appear in the derivation chain. The conservative accretion setup is an explicit modeling choice whose sensitivity is acknowledged but does not create a circular reduction.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The model rests on the standard FLRW metric, the future event horizon as IR cutoff, and the specific form of Kaniadakis entropy; the accretion history and plasma dispersion are additional modeling choices not derived from first principles.

free parameters (3)

alpha (EGB coupling)
Fitted to cosmological data; best-fit ~ -0.004
c (holographic parameter)
Fitted; best-fit ~1.18
beta (Kaniadakis parameter)
Fitted; best-fit ~2.26 with large uncertainty

axioms (2)

domain assumption Future event horizon as infrared cutoff for holographic dark energy
Stated in abstract as the adopted cutoff
standard math FLRW background with standard matter and radiation components
Implicit in cosmological evolution equations

pith-pipeline@v0.9.0 · 5660 in / 1655 out tokens · 29896 ms · 2026-05-17T04:44:12.136877+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel contradicts

?

contradicts
CONTRADICTS: the theorem conflicts with this paper passage, or marks a claim that would need revision before publication.

We adopt Kaniadakis statistics... S_κ = 1/β sinh(β S_BH)... ρ_DE = 3H²M_p² (c²/y² + β² y²/3)
IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

modified Friedmann equation H² + α H⁴ = 8πG/3 (ρ_m + ρ_DE)

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Reference graph

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