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Late-time cosmological constraints on three holographic dark energy models with DESI DR2 BAO and Type Ia supernovae

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Pith's one-line read Late-time DESI DR2 and supernova data leave three holographic dark energy models near ΛCDM and do not ease the Hubble tension.

desk verdict Solid late-time MCMC update of HDE/ADE/RDE with DESI DR2: none raise H0, HDE is the least awkward of the three, and the authors stay inside their data. read the letter →

arxiv 2607.09732 v1 pith:WB2QNHDB submitted 2026-07-02 physics.gen-ph

Jiayuan Huang , Tonghua Liu , Chenggang Shao This is my paper
classification physics.gen-ph
keywords holographicdarkenergyagegraphicRicciDESIDR2BAOHubbletensionTypeIasupernovaeredshift-spacedistortionslate-timecosmology
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tests three dark energy models inspired by the holographic principle—holographic, agegraphic, and Ricci dark energy—against current late-time cosmic data only. The authors combine cosmic chronometers, three Type Ia supernova samples, DESI DR2 baryon acoustic oscillations, and redshift-space distortion growth measurements, treating the sound horizon as free so early-universe priors are not imposed. They find that holographic dark energy is driven toward a near-de Sitter expansion, agegraphic dark energy sits at a stable age scale, and Ricci dark energy persistently prefers a low matter density. All three still give Hubble constants around 67–68 km/s/Mpc, close to early-universe inferences and far from the higher local ladder value. Information criteria do not show a decisive preference for any of them over the standard cosmological constant model. A sympathetic reader cares because these are among the few dynamical dark energy proposals with a clear physical cutoff scale, and the analysis asks whether that scale still looks necessary once DESI DR2 is included.

What carries the argument

The holographic cutoff construction itself: dark energy density is set by an infrared scale (future event horizon for HDE, conformal age for ADE, Ricci scalar for RDE), which fixes the functional form of E(z) and wde(z) once a single dimensionless parameter is chosen, then fitted jointly with free rd via MCMC.

What would settle it

A joint analysis that includes CMB likelihoods plus full linear perturbations for the same three models: if the preferred late-time solutions (especially RDE’s low matter density and high fitted σ8,0) become incompatible with the CMB and growth spectrum, or if holographic dark energy is no longer near c = 1, the claim that late-time data leave them near ΛCDM without easing the Hubble tension would be overturned.

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Extended reading notes

Core claim

When constrained by late-time H(z), SNe Ia, DESI DR2 BAO, and an RSD growth compilation with free sound horizon, none of the three holographic-inspired models significantly alleviates the Hubble tension. Holographic dark energy is driven to c ≃ 1 (near the de Sitter boundary), agegraphic dark energy to n ≃ 2.8, and Ricci dark energy to γ ≃ 0.53–0.55 with Ωm0 ≃ 0.215–0.219; holographic dark energy is the most balanced of the three, yet current data do not decisively prefer it over ΛCDM.

Load-bearing premise

The growth check uses only the standard general-relativistic linear growth equation with free present-day fluctuation amplitude and is not a full stability analysis of how these dark energy models actually perturb.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

0 major / 5 minor

Summary. The paper presents a late-time Bayesian MCMC analysis of three holographic-inspired dark energy models (HDE, ADE, RDE) using cosmic chronometers, three SNe Ia compilations (Pantheon+, DES-Dovekie, DESY5), DESI DR2 BAO, and an extended RSD fσ8 compilation. Five data combinations are studied, with rd free in BAO-included runs and σ8,0 free only when RSD is included. Posteriors (Table II) show HDE driven to c≃1 with H0≃67–68 km s−1 Mpc−1 and Ωm0≃0.27, ADE with n≃2.8 and slightly lower H0, and RDE with γ≃0.53–0.55 but persistently low Ωm0≃0.215–0.219. The authors reconstruct wde(z), quantify the H0–rd degeneracy, report AIC/BIC relative to ΛCDM, and conclude that none of the models significantly alleviates the Hubble tension and that late-time data do not decisively prefer them over ΛCDM, with HDE the most balanced of the three.

Significance. If the results hold, the paper provides a clean, carefully scoped late-time comparison of three standard holographic DE constructions against current DESI DR2 BAO and modern SNe samples. Strengths include free-rd treatment (avoiding CMB sound-horizon priors), full CC and SN covariance matrices, explicit ΛCDM baselines for the same combinations, transparent reporting of ΔAIC/ΔBIC, and explicit labeling of the RSD analysis as a growth consistency check rather than a full perturbation-level stability test. The work is useful as a phenomenological benchmark for the community and correctly refrains from overclaiming resolution of the Hubble tension or decisive preference over ΛCDM.

minor comments (5)
  1. In Sec. III.D and IV.C the authors correctly state that the RSD analysis uses the standard GR linear growth equation (Eq. 32) and is not a full perturbative stability analysis, especially for RDE. A single clarifying sentence in the abstract or conclusions restating that the reported σ8,0 values are nuisance amplitudes for the adopted growth data (not model predictions from a complete DE perturbation sector) would further reduce possible misreading.
  2. Table II: for ADE the Ωm0 column is blank by construction (fixed by flatness and E(0)=1). A brief footnote or table note stating that Ωm0 is derived rather than free would help readers scanning the table.
  3. Fig. 4 and Table IV: the derived weffa is a low-redshift CPL projection with w0 fixed, not a free CPL fit. The text already says this; ensuring the table caption repeats the caveat would make the comparison with DESI CPL discussions harder to misinterpret.
  4. Minor typographical/formatting issues: “Observational Data” and “Statistical Methodology” appear with spaced letters in the section heading; “DESI R2” once appears instead of “DESI DR2”; and a few references (e.g. the DES-Dovekie arXiv entry) may need final bibliographic polishing.
  5. The extended RSD compilation is heterogeneous. A short sentence listing which points enter the covariance (or a reference to the exact compilation used) would improve reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: independently defined holographic models are fitted to late-time data; derived w_de(z) and weff_a are explicit projections of those fits, not tautologies.

full rationale

The paper defines HDE, ADE and RDE from standard holographic constructions (Eqs. 2–19: future-event-horizon cutoff, conformal age, Ricci scalar) that do not depend on the observational data sets. Free parameters (H0, Ωm0 or n/γ/c, rd, σ8,0) are sampled via MCMC against CC+SNe+DESI DR2 BAO (+RSD) combinations; posteriors, AIC/BIC differences, and reconstructed w_de(z) (Fig. 4) are ordinary outputs of that fit. The derived weff_a values (Table IV) are explicitly labeled low-redshift CPL projections of the model trajectories, not independent predictions. The H0–rd anti-correlation (Fig. 5) is the expected geometric degeneracy when rd is left free; the paper quantifies it and does not claim a CMB-calibrated H0. The RSD fσ8 check uses the standard GR growth equation with free σ8,0 and is repeatedly caveated as a consistency test only. No self-definitional loop, fitted-input-as-prediction, load-bearing self-citation of an unproven uniqueness claim, or renaming of a known result appears. The analysis is a conventional late-time phenomenological comparison and is self-contained against external benchmarks.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

The work is a standard late-time parameter-estimation exercise. All free parameters are the usual cosmological and model parameters fitted by MCMC; the axioms are the pre-existing holographic constructions plus flat FRW and linear GR growth. No new physical entities are postulated.

free parameters (7)
  • H0 = ≈66.5–68.0 km s⁻¹ Mpc⁻¹ (BAO-included)
    Present-day Hubble constant; fitted freely in every combination (prior [50,90]).
  • Ωm0 = HDE ≈0.270–0.272; RDE ≈0.215–0.219
    Present matter density; free for HDE and RDE, derived for ADE.
  • c (HDE) = ≈0.99–1.09 (BAO-included)
    Holographic parameter controlling IR-cutoff strength; free prior [0.1,3].
  • n (ADE) = ≈2.78–2.81
    Agegraphic parameter; free prior [0.1,5].
  • γ (RDE) = ≈0.53–0.55
    Ricci-curvature coupling; free prior [0.01,1].
  • rd = ≈146.6–147.2 Mpc
    Sound-horizon scale treated as free late-time parameter (prior [130,160] Mpc).
  • σ8,0 = HDE 0.875; ADE 0.893; RDE 0.961
    Present fluctuation amplitude; free nuisance only in RSD combination.
assumptions (6)
  • domain assumption Spatially flat FRW background with cold dark matter, radiation and dark energy.
    Stated at the opening of Sec. II; used for all E(z) expressions.
  • domain assumption Holographic dark-energy density ρde = 3c² Mp² L⁻² with L = future event horizon.
    Eq. (2) and following; taken from Li (2004).
  • domain assumption Agegraphic density ρde = 3n² Mp² η⁻² with η conformal time.
    Eq. (6); taken from Wei & Cai (2008).
  • domain assumption Ricci dark-energy density ρde = 3γ Mp² (Ḣ + 2H²).
    Eq. (12); taken from the RDE literature.
  • domain assumption Linear growth of matter perturbations obeys the standard GR equation (32).
    Sec. III.D; used for the fσ8 likelihood.
  • standard math AIC = χ²min + 2k and BIC = χ²min + k ln N are appropriate model-selection metrics.
    Sec. III.E; standard information criteria.

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Pith. "Pith review of Late-time cosmological constraints on three holographic dark energy models with DESI DR2 BAO and Type Ia supernovae." pith.science (2026). https://pith.science/paper/WB2QNHDB

@misc{pith2026260709732,
  author       = {Pith},
  title        = {Pith review of: Late-time cosmological constraints on three holographic dark energy models with DESI DR2 BAO and Type Ia supernovae},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WB2QNHDB}},
  note         = {Machine review of arXiv:2607.09732}
}
abstract

We constrain three holographic-inspired dark energy models, namely holographic dark energy (HDE), agegraphic dark energy (ADE), and Ricci dark energy (RDE), using late-time observations from cosmic chronometers, Type Ia supernovae (SNe Ia), DESI DR2 baryon acoustic oscillations (BAO), and {redshift-space distortion (RSD) growth measurements}. Five data combinations are considered: $H(z)+$Pantheon+, $H(z)+$DESI DR2+Pantheon+, $H(z)+$DESI DR2+DES-Dovekie, $H(z)+$DESI DR2+DESY5, and {$H(z)+$DESI DR2+DES-Dovekie+RSD}. We perform Bayesian Markov chain Monte Carlo parameter estimation and compare the models with AIC and BIC. In the BAO-included combinations, HDE gives $H_0\simeq67.3$--$68.0~\mathrm{~km~s^{-1}~Mpc^{-1}}$, $\Omega_{m0}\simeq0.270$--$0.272$, and $c\simeq1$, indicating an expansion history close to the de Sitter boundary rather than a robust phantom regime. ADE yields a stable agegraphic parameter $n\simeq2.78$--$2.81$, while RDE gives $\gamma\simeq0.53$--$0.55$ and persistently favors a low matter density, $\Omega_{m0}\simeq0.215$--$0.219$. {Treating $r_d$ as a free parameter reveals a strong negative correlation between $H_0$ and $r_d$, and the RSD-included combination provides a growth-level consistency check through $f\sigma_8(z)$ without constituting a full perturbative stability analysis.} None of the three models significantly alleviates the Hubble tension. Overall, HDE shows the most balanced phenomenological behavior among the three models, although current late-time data do not decisively prefer it over $\Lambda\text{CDM}$.

Figures

Figures reproduced from arXiv: 2607.09732 by the authors.

Figure 1
Figure 1. shows the 1σ and 2σ confidence contours of HDE for the five data combinations. The corresponding posterior constraints are summarized in Table II. For the first four data combinations, the constraints remain con￾sistent with the background-only results discussed above. For the H(z)+DESI DR2+DES-Dovekie+RSD combi￾nation, we obtain H0 = 67.860+1.534 −1.579 km s−1 Mpc−1 , Ωm0 = 0.270+0.009 −0.008, c = 1.011+0.076 −0.07… view at source ↗
Figure 2
Figure 2. shows the confidence contours of ADE from different data combinations, with posterior constraints listed in Table II. For the first four data combinations, the constraints remain consistent with the background￾only results discussed above. For the H(z)+DESI DR2+DES-Dovekie+RSD combination, we obtain H0 = 66.734+1.591 −1.579 km s−1 Mpc−1 , n = 2.804+0.042 −0.042, rd = 147.075+3.529 −3.323 Mpc, and σ8,0 = 0.893+0.035 … view at source ↗
Figure 3
Figure 3. , with posterior constraints summarized in Ta￾ble II. For the first four data combinations, the constraints remain consistent with the background￾only results discussed above. For the H(z)+DESI DR2+DES-Dovekie+RSD combination, we obtain H0 = 67.822+1.655 −1.691 km s−1 Mpc−1 , Ωm0 = 0.216+0.007 −0.007, γ = 0.540+0.017 −0.017, rd = 146.988+3.563 −3.344 Mpc, and σ8,0 = 0.961+0.043 −0.041. Across all data combinations, … view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Redshift evolution of the dark energy equation-of-state parameter [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: RSD measurements of [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]

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