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The paper claims that a small shortfall in the universe's horizon entanglement entropy—relative to its Bekenstein–Hawking value—would produce a late-time boost in cosmic expansion that can ease the Hubble tension, without touching the early

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2026-08-03 08:08 UTC pith:O5LJXAHT

load-bearing objection A transparent consistency test that masquerades as a detection: the HEED amplitude is inherited from the SH0ES anchor, not earned by the data. the 3 major comments →

arxiv 2601.17938 v3 pith:O5LJXAHT submitted 2026-01-25 astro-ph.CO gr-qchep-phhep-th

Hubble Tension as an Effect of Horizon Entanglement Nonequilibrium

Alexander S. Sakharov , Rostislav Konoplich , Merab Gogberashvili , Jack Simoni This is my paper
classification astro-ph.CO gr-qchep-phhep-th PACS 98.80.-k98.80.Es
keywords horizon entanglement entropyHubble tensionBekenstein–Hawking entropyapparent horizonentanglement equipartition deficitdark energyintegrated Sachs–Wolfe effectcosmological background
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper proposes that the apparent (Hubble) horizon of the late universe is slightly out of entanglement equilibrium: the actual entanglement entropy across it falls short of the Bekenstein–Hawking value by a fraction δ(a). That shortfall, converted through equipartition at the horizon temperature, adds a smooth energy density proportional to H²/G, which is negligible at early times but switches on at redshifts z≲1 and raises the expansion rate by a few percent. This would reconcile higher local measurements of H0 with CMB constraints from the early universe, because recombination and the sound horizon are untouched. The authors test the idea against supernova distances, baryon acoustic oscillations, cosmic chronometer H(z) data, and redshift-space distortion growth measurements, and find the model can accommodate a high late-time Hubble rate without spoiling established distance and growth constraints, though the current data cannot decisively prefer it over standard cosmology.

Core claim

The central claim is that the horizon entanglement equipartition deficit (HEED) supplies a physical origin for a holographic-style dark energy. Starting from a fractional deficit δ(a)=1−S_ent/S_BH at the apparent horizon, and applying equipartition with the Gibbons–Hawking temperature T=H/(2π) to the missing surface degrees of freedom, the paper derives a bulk density ρ_HEED = (3/8πG) c_e²(a) H²(a) with c_e²(a) = 2δ(a). Because ρ tracks H², it is automatically small at early times; a smooth late-time activation g(a; a_t, k) makes it switch on at z≲1. The net effect is a rescaling of the Friedmann equation H² = (8πG/3)(ρ_m+ρ_Λ)/(1−c_e²(a)), which boosts the present-day expansion rate by (1−c_

What carries the argument

The central object is the horizon entanglement equipartition deficit (HEED): a fractional shortfall δ(a)=1−S_ent/S_BH of the renormalized entanglement entropy across the apparent horizon relative to the Bekenstein–Hawking entropy A/(4G). The machinery is the equipartition identity ΔE_surf = (1/2)δ N_surf T_dS with N_surf = A/G and T_dS = H/(2π), which turns the entropy deficit into a surface energy deficit and then, divided by the Hubble volume, into a homogeneous bulk density scaling as H²/G. A three-parameter activation function c_e²(a)=c_e0 (1+(a_t)^k)/(1+(a_t/a)^k) controls the late-time switch-on; this function is what lets the component be negligible at recombination and active today.

Load-bearing premise

The load-bearing premise is that a fractional deficit δ(a) of the horizon's entanglement entropy relative to Bekenstein–Hawking actually exists in the late universe and follows the assumed smooth activation, and that the equipartition counting maps that deficit to a bulk energy density exactly as assumed; without an independent derivation of δ(a), the H0 boost is a fitted constant.

What would settle it

A direct calculation showing that the renormalized entanglement entropy across the apparent horizon exactly saturates the Bekenstein–Hawking value for the late-time FLRW state would eliminate the deficit and the model. Observationally, a precise measurement of the late integrated Sachs–Wolfe effect (via CMB–galaxy cross-correlation) that finds no enhancement over ΛCDM at the level predicted for c_e0 ≈ 0.06–0.10 would falsify HEED's growth side.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • At z≲1, HEED raises H(z) by a few percent; H0 is boosted by (1−c_e0)^(−1/2) — about 3% for c_e0=0.06 and 5% for c_e0=0.10.
  • Recombination physics and the sound horizon are preserved, so the early-universe ruler that anchors the CMB Hubble estimate is unchanged.
  • The model predicts a mild suppression of fσ8(z) at low z and a correspondingly enhanced late integrated Sachs–Wolfe effect, offering growth-based tests.
  • Fits to supernovae, BAO, cosmic chronometer, and RSD data show HEED can accommodate an anchored late-time H0 near 73 km/s/Mpc while remaining consistent with distance and growth constraints.
  • The posterior favors c_e0 > 0 with activation at z_t ~ 0.7–1.5, but the sharpness k is poorly constrained and HEED is not statistically preferred over ΛCDM at current precision.

Where Pith is reading between the lines

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

  • If HEED is right, the Hubble tension is not an early-universe problem at all: it is a late-time horizon information deficit, which would sidestep the sound-horizon pressures that constrain early dark energy.
  • A sharp test would be the late ISW signal: HEED predicts enhanced ISW beyond what a smooth dark energy with the same expansion history would produce, measurable through CMB–large-scale-structure cross-correlations; the paper notes but does not perform this analysis.
  • The equipartition step is a bookkeeping translation; without an independent microphysical calculation of δ(a) from, say, horizon mutual information or entanglement wedge capacity, the model is a physically motivated reparameterization of a late-time constant.
  • The mild growth suppression and lower σ8 favored by the fit suggest HEED could also soften the S8 tension, though the paper presents this only as a possible bonus.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper proposes a late-time infrared mechanism, HEED, to alleviate the Hubble tension. It argues that a small deficit δ(a) in horizon entanglement entropy relative to the Bekenstein–Hawking value, mapped through horizon equipartition, sources a homogeneous component with ρ_HEED ∝ c_e^2(a) H^2(a), where c_e^2(a)=2δ(a). A three-parameter activation model for c_e^2(a) is introduced, and the background expansion, effective equation of state, and linear growth are derived. The model is fitted to SN Ia, BAO, cosmic chronometer, and RSD data, with an external Gaussian prior on the effective Hubble scale H_eff^0=73 km/s/Mpc. The analysis finds c_e0>0 and late-time activation, but the paper itself notes that the best-fit HEED and ΛCDM curves are nearly indistinguishable and frames the exercise as an 'anchored consistency test'.

Significance. If a genuine IR entanglement deficit were established, the H^2/G scaling would be an interesting way to modify late-time expansion without affecting recombination, with testable consequences for H(z), fσ8(z), and the ISW effect. The paper's background algebra and growth equations are standard, and the data compilation is extensive. However, the central claim that HEED is an effect causing the boosted late-time H0 is not supported by the presented evidence: the nonzero c_e0 is induced by the imposed SH0ES anchor rather than required by the data, and no model comparison is provided. The authors' candid statement that the chains do not infer an upward shift is commendable, but it directly undercuts the title and abstract's causal language.

major comments (3)
  1. [Sec. III.B, Eq. (27) and Eq. (41)] The central evidence for a nonzero HEED amplitude is circular. The posterior is conditioned on an external Gaussian prior on H_eff^0 centered at 73 km/s/Mpc (Eq. 41), and Eq. (27) defines H_eff^0 = H_0 / sqrt(1 - c_e0^2). For any underlying H_0 < 73, this anchor is satisfied by c_e0^2 = 1 - (H_0/73)^2. The text itself states that 'the chains do not infer an upward shift of the Hubble scale relative to CMB-only analyses.' The reported posterior peak of c_e0 away from zero is therefore a reparameterization of the SH0ES prior, not 'direct phenomenological support' for a horizon entanglement deficit, as claimed in Sec. III.B. This invalidates the title/abstract claim that HEED is an effect causing the boosted late-time H0.
  2. [Sec. III.B, Figs. 4-8] No model comparison with ΛCDM is presented. The paper states that best-fit HEED and ΛCDM curves are nearly indistinguishable at current precision, yet no Δχ², AIC/BIC, DIC, or Bayes factor is reported. Without such a statistic, the analysis can at most show that HEED is not excluded by low-z data; it cannot show that the data favor HEED over ΛCDM or that HEED alleviates the Hubble tension. A free fit without the H_eff^0 anchor, or a joint analysis that treats H0 as a parameter to be inferred, is required to establish an upward shift in the expansion rate.
  3. [Sec. II, Eqs. (10)-(14) and Eq. (17)] The physical identification of c_e^2(a) with an entanglement entropy deficit δ(a) is not derived from an underlying model. The equipartition step ΔE_surf = (1/2)δ N_surf T_dS assumes that horizon degrees of freedom are counted by N_surf = A/G and that a fractional deficit in S_ent maps linearly to a missing surface energy. No microphysical mechanism for δ(a) is provided, and the activation function g(a;a_t,k) in Eq. (17) is ad hoc. This is acceptable for a phenomenological parameterization, but it means that the current HEED 'effect' is a fitted H^2-proportional component, not a demonstrated consequence of horizon entanglement nonequilibrium. The paper should explicitly state this limitation whenever drawing physical conclusions.
minor comments (4)
  1. [Sec. I] The paragraph beginning 'Two features make HEED cosmologically attractive...' appears twice nearly verbatim in the Introduction.
  2. [Fig. 3] The axis label '2 Ceo' appears garbled and should read 'c_e0^2' or similar. Figures 1 and 2 also lack full caption text in the provided manuscript.
  3. [Sec. III.A, Eqs. (34)-(36)] The BAO, CC, and RSD likelihoods are taken as diagonal Gaussian forms. The compressed BAO points from BOSS/eBOSS/DESI may have nontrivial correlations; the paper should justify the diagonal approximation or use the published covariances.
  4. [Sec. III.A general] The MCMC setup is described but convergence diagnostics are not reported (chain length, burn-in, acceptance fractions, Gelman-Rubin or similar). This limits reproducibility of the posterior results.

Circularity Check

1 steps flagged

The claimed HEED signal is not independently inferred: the nonzero c_e0 peak is induced by the H_eff0=73 anchor via Eqs. (41) and (27), and the reported H0 boost is that anchor relabeled.

specific steps
  1. fitted input called prediction [Sec. III.A, Eq. (41); Sec. III.B, 'Present-day HEED amplitude']
    "Finally, in anchored analysis we impose an external Gaussian prior on the effective Hubble scale H_eff0, not on H0, χ²_H_eff0 = ((H_eff0 − H_eff0,⋆)/σ_H_eff0)², H_eff0 = H0/sqrt(1−c_e0²). (41) This prior is not used to infer the Hubble scale from low-z probes alone. Rather, it enables a consistency test ... A central result of the analysis is that the posterior for the HEED amplitude c_e0 peaks decisively away from zero. Pure ΛCDM, corresponding to c_e0 = 0, lies in the tail of the posterior ... This provides direct phenomenological support for a nonvanishing late-time horizon entanglement def"

    The posterior is conditioned on H_eff0 = 73 (Eq. 41). By the paper's own definition Eq. (27), H_eff0 ≡ H0/sqrt(1−c_e0²), so any underlying H0 below 73 is converted into c_e0>0 through c_e0² = 1−(H0/73)². Hence the 'central result' that c_e0 peaks away from zero is the imposed SH0ES anchor rewritten in the new coordinates, not an independent inference from the low-z data. The claimed Hubble boost H_eff0/H0=(1−c_e0²)^−1/2 is the same defining relation, so the 'prediction' reduces to the input prior. The paper itself concedes this is 'an anchored consistency test (high H_eff0 imposed), rather than as a free low-z determination of the Hubble scale.'

full rationale

The formal map from an assumed fractional deficit δ(a) to ρ_HEED via horizon equipartition (Eqs. 9–14) is algebraically self-contained and not circular; it uses standard horizon thermodynamics and is not carried by self-citations of the present authors. The circularity is located in the observational claim. Eq. (41) imposes a Gaussian prior on H_eff0, and Eq. (27) defines H_eff0=H0/sqrt(1−c_e0²). This means the nonzero c_e0 reported as 'direct phenomenological support' for an entanglement deficit is the H_eff0=73 anchor transformed through the model coordinates, especially because the chains are not free determinations of H_eff0. The associated fσ8 suppression and H(z) boost are consequences of the fitted activation parameters, not independent predictions; the paper itself states that best-fit HEED and ΛCDM curves are nearly indistinguishable at current precision, and it defers both a full model comparison with ΛCDM and a microphysical model of δ(a) to future work. Thus the central headline inference—that horizon entanglement nonequilibrium causes the late-time H0 boost—is partially circular: the algebraic δ→ρ relation is noncircular, but the evidence for a nonzero δ reduces to a reparameterization of the imposed prior.

Axiom & Free-Parameter Ledger

3 free parameters · 4 axioms · 1 invented entities

The model introduces three fitted parameters (c_e0, a_t, k) and postulates a new entity δ(a) without microphysical derivation. The standard horizon-thermodynamics assumptions are domain-level; the load-bearing assumptions are the existence of the deficit and the equipartition mapping, both ad hoc to this paper.

free parameters (3)
  • c_e0 = posterior peaks away from zero (exact value not quoted)
    Present-day HEED amplitude; directly controls the H0 boost via Eq. (27); fitted to SN+BAO+CC+RSD under the H_eff^0 prior.
  • a_t = posterior ~0.4–0.6
    Activation epoch; sets the redshift at which the deficit switches on; fitted, constrained to late times by the early-time safety prior.
  • k = weakly constrained, possibly multi-modal
    Sharpness of the switch-on; effectively a nuisance parameter at current precision.
axioms (4)
  • domain assumption The apparent Hubble horizon has a temperature T_dS = H/(2π) and Bekenstein–Hawking entropy S_BH = A/(4G), and equipartition E = (1/2) N T applies to its effective degrees of freedom.
    Used in Eqs. (10)–(13) to convert the deficit δ into an energy density. This is standard horizon thermodynamics but an assumption about the applicability of equipartition to a cosmological horizon.
  • ad hoc to paper A fractional deficit δ(a) ∈ [0,1] of the renormalized horizon entanglement entropy exists in the late universe and follows the ad hoc activation g(a;a_t,k) of Eq. (17).
    No microphysical derivation is provided; the authors state that microphysical models would 'move HEED from a phenomenological IR mechanism toward a predictive, first principles account.' The entire late-time effect rests on this postulate.
  • ad hoc to paper The UV area-law contribution to entanglement entropy renormalizes 1/G while the IR deficit sources a new fluid, so the two can be separated without double-counting.
    Invoked in Sec. II and Appendix A; the split is physically plausible but is an assumption about the renormalization scheme.
  • domain assumption The HEED sector is smooth and non-clustering (rest-frame sound speed ≃1), so linear growth is computed with the standard GR ODE (Eq. 21).
    Needed for the fσ8 predictions; the paper explicitly treats HEED as a non-propagating effective background.
invented entities (1)
  • Horizon entanglement equipartition deficit δ(a) (equivalently the HEED fluid ρ_HEED) no independent evidence
    purpose: A new, time-dependent source of energy density proportional to H²/G, responsible for a late-time boost in the expansion rate.
    The only quantitative handle on δ(a) is the fitted amplitude and activation parameters; the predicted ISW enhancement is qualitative and not tested. There is no independent measurement or microphysical prediction that could falsify the entity outside the model's own fit.

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read the original abstract

We propose an infrared mechanism for alleviating the Hubble constant tension, based on a small departure from entanglement equilibrium at the cosmological apparent horizon. If the horizon entanglement entropy falls slightly below the Bekenstein-Hawking value, we parametrize the shortfall by a fractional deficit $\delta(a)$ evolving with the FLRW scale factor $a$. The associated equipartition deficit at the Gibbons-Hawking temperature then sources a smooth, homogeneous component whose density scales as $H^{2}/G$, with a dimensionless coefficient $c_{e}^{2}(a)$ of order unity times $\delta(a)$. Because this component tracks $H^{2}$, it is negligible at early times but can activate at redshifts $z\lesssim 1$, raising the late time expansion rate by a few percent without affecting recombination or the sound horizon. We present a minimal three parameter activation model for $c_{e}^{2}(a)$ and derive its impact on the background expansion, effective equation of state, and linear growth for a smooth entanglement sector. The framework predicts a small boost in $H(z)$, a mild suppression of $f\sigma_{8}(z)$, and a corresponding modification of the low-$z$ distance-redshift relation. We test these predictions against current low-redshift data sets, including SN~Ia distance moduli, baryon acoustic oscillation distance measurements, cosmic chronometer $H(z)$ data, and redshift space distortion constraints, and discuss whether the $H_0$ tension can be consistently interpreted as a late-time, horizon-scale information deficit rather than an early universe modification.

Figures

Figures reproduced from arXiv: 2601.17938 by Alexander S. Sakharov, Jack Simoni, Merab Gogberashvili, Rostislav Konoplich.

Figure 1
Figure 1. Figure 1: FIG. 1. HEED’s linear growth impact illustrated for three [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Triangle plot for the HEED parameterization showing the marginalized posterior distributions of [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Pantheon+ SN Ia distance moduli [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. BAO measurements of the radial (line-of-sight) co [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. RSD growth constraints in the HEED framework. Measurements of [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗

discussion (0)

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Modifying $\Lambda$CDM dynamics via out-of-equilibrium axions: reconciling SH0ES and DESI $H_0$ values

    astro-ph.CO 2026-06 unverdicted novelty 5.0

    Out-of-equilibrium axion dark matter modifies late-time expansion to reconcile SH0ES H0 ≈ 73 km/s/Mpc with DESI BAO data while recovering standard behavior at higher redshifts.

  2. Modifying $\Lambda$CDM dynamics via out-of-equilibrium axions: reconciling SH0ES and DESI $H_0$ values

    astro-ph.CO 2026-06 conditional novelty 5.0

    A two-parameter model in which axion dark matter is driven out of equilibrium at late times fits SH0ES and DESI data with H0 ≈ 73 km/s/Mpc, but only when the SH0ES prior is included.

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