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A Model of Holographic Dark Energy

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Miao Li

High Energy Physics - Theory · Submitted 11 Mar 2004 · 9 references

Pith's verdict: The future-event-horizon cutoff is a real and correct fix to Hsu's w=0 problem, and the w=-0.90 prediction is genuine — but it is conditional on a heuristic c=1, and the coincidence 'resolution' reads N off the data.

T0 · AI review

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arXiv IDhep-th/0403127 (version 4)
Pith IDAX5R5GJX, Pith's permanent record of this paper and its review
CitationMiao Li. "A Model of Holographic Dark Energy." arXiv:hep-th/0403127 (2004). https://pith.science/paper/AX5R5GJX
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The paper

The paper claims

The dark energy accelerating the universe may be a quantum vacuum energy whose size is fixed by the future event horizon, and that single choice turns a failed holographic idea into a model that predicts the equation of state $w=-0.90$ at $

The reading

The paper asks whether the dark energy that accelerates the universe can be a quantum vacuum energy whose magnitude is not arbitrary but set by a horizon, using the same logic that says no region can hold more energy than a black hole of its size. Earlier attempts used the Hubble scale as that horizon and failed: the resulting dark energy tracked matter exactly and had zero pressure, so it could not accelerate anything. Miao Li shows that if the cutoff is instead the future event horizon, the largest distance a comoving observer will ever be able to see, the same holographic relation produces genuine acceleration, with an equation of state $w = -1/3 - 2/(3c)$ that is below $-1/3$ for any positive $c$. Fixing the one free constant to $c=1$ through a black-hole saturation argument and feeding in the observed $Ω_Λ = 0.73$ yields a parameter-free prediction $w = -0.903 + 0.104z$ near the present epoch, close to what supernova data already indicate. The author also argues that inflation redshifts any initial holographic energy density by roughly $e^{-2N}$, so with the minimal $N=60$ e-folds the coincidence problem becomes a consequence of inflation rather than a fine-tuning, though he calls that estimate rough and defers a detailed treatment to later work.

What carries the argument

The load-bearing object is the future event horizon, the boundary of the spacetime volume a fixed observer can ever see, used as the infrared cutoff in the holographic energy density. Two supporting pieces carry the argument: a saturation argument that equating the energy inside a sphere of radius $R_h$ with the mass of a black hole of that radius, $ρ_Λ = 3M_p^2 R_h^{-2}$, fixes $c=1$; and an exact rewriting of the horizon definition into a differential equation for $Ω_Λ$, $Ω_Λ' / Ω_Λ^2 = (1-Ω_Λ)(1/Ω_Λ + 2/(c√{Ω_Λ}))$, which is integrable in closed form and yields both the late-time approach to a cosmological constant and the early-time behavior $ρ_Λ ∝ a^{-2}$.

Extended reading notes

Core claim

The central claim is that the holographic bound $ρ_Λ = 3c^2 M_p^2 L^{-2}$ becomes a working model of dark energy if and only if $L$ is taken to be the future event horizon $R_h = a∫_a^∞ da'/(Ha'^2)$ rather than the Hubble scale or the particle horizon. With the event horizon, the Friedmann equation plus the holographic relation close into an exact integral equation for $H(a)$, which the author converts into a first-order differential equation for the dark-energy fraction $Ω_Λ$; that equation has $Ω_Λ$ increasing monotonically toward 1 and never turning over, so the universe accelerates and does not recollapse. In the dark-energy-dominated limit the equation of state is $w = -1/3 - 2/(3c)$, which is $-1$ at $c=1$; keeping matter and expanding about the present epoch gives $w = -0.903 + 0.104z$ for $Ω_Λ^0 = 0.73$, a number the author presents as a falsifiable prediction rather than a fit.

Load-bearing premise

The headline number $w=-0.90$ depends on setting $c=1$, and that value is fixed by equating the energy inside a sphere of the horizon's radius with the mass of a black hole of that size, which is a plausibility argument rather than a derivation; any other $c$ moves the prediction to $w=-1/3-2/(3c)$.

Editorial extensions

If this is right

  • The equation of state is predicted as a function of redshift, not just today: $w = -0.903 + 0.104z$ for $c=1$ and $Ω_Λ^0 = 0.73$, so a measurement at $z≈0.5$ tests the model where it deviates most from a pure cosmological constant.
  • The final, asymptotic cosmological constant is fixed by the present matter density through $ρ_Λ = 3^8 2^{-4} e^{3x_0} ρ_m^0$, so the model converts a boundary condition at the present epoch into a prediction for the far future.
  • The sign of $c-1$ is tied to thermodynamics: $c<1$ gives phantom behavior $w<-1$ and a shrinking horizon whose entropy decreases, violating the second law, while $c>1$ preserves the second law but loses the de Sitter symmetry, which is why the author settles on $c=1$.
  • In the early universe the holographic energy scales as $a^{-2}$ and stays subdominant to radiation and matter, so big bang nucleosynthesis and the standard expansion history are left intact.
  • Inflation with the minimal $N=60$ e-folds suppresses the dark-energy-to-radiation ratio to about $10^{-52}$, so the observed near-equality of dark energy and matter today follows from the amount of inflation rather than from a tuned initial condition.

Reading between the lines

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

  • Because the prediction is a one-parameter family $w = -1/3 - 2/(3c)$, measuring $w$ at two well-separated redshifts would fix both $c$ and $Ω_Λ$ and turn the model into a closed test, rather than a curve fitted at a single epoch.
  • The model is designed to look like a cosmological constant in the far future and to differ from it most around $z∼1$; that is precisely the window where the next generation of distance and growth measurements has the most leverage, so the decisive data are not yet in hand.
  • The early-time $a^{-2}$ scaling is the same as the scaling of a free massless scalar's kinetic energy, so at high redshift this model can be mimicked by an ordinary light field; separating the two requires resolving the transition region rather than the asymptotic behavior.
  • The author's conformal-time argument, that the event horizon is a finite box rather than an acausal influence, is the same reasoning used for horizon entropy; if it holds, the model predicts that horizon entropy should never decrease, which is itself an observational statement about the sign of $c-1$.
Original abstract

A model for holographic dark energy is proposed, following the idea that the short distance cut-off is related to the infrared cut-off. We assume that the infrared cut-off relevant to the dark energy is the size of the event horizon. With the input $\Omega_\Lambda=0.73$, we predict the equation of state of the dark energy at the present time be characterized by $w=-0.90$. The cosmic coincidence problem can be resolved by inflation in our scenario, provided we assume the minimal number of e-folds.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,558 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.55 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.06 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v4. Results and the main claim are underlined; .

A model for holographic dark energy is proposed, following the idea that the short distance cut-off is related to the infrared cut-off. We assume that the infrared cut-off relevant to the dark energy is the size of the event horizon. With the input $\Omega_\Lambda=0.73$, we predict the equation of state of the dark energy at the present time be characterized by $w=-0.90$. The cosmic coincidence problem can be resolved by inflation in our scenario, provided we assume the minimal number of e-folds.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 A model for holographic dark energy is proposed, following the idea that the short distance cut-off is related to the infrared cut-off. contribution 0.95 0.76 0.13 asserted 0.95
s1 We assume that the infrared cut-off relevant to the dark energy is the size of the event horizon. method 0.86 0.64 0.08 asserted 0.87
s2 With the input $\Omega_\Lambda=0.73$, we predict the equation of state of the dark energy at the present time be characterized by $w=-0.90$. result 1.00 0.89 0.34 asserted 0.91
s3 The cosmic coincidence problem can be resolved by inflation in our scenario, provided we assume the minimal number of e-folds. interpretation 0.69 0.59 0.15 hedged possibility 0.85

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.74.

What was examined, and what was not

sources read
  • arXiv listing abstract v4
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References
How later papers used it

230 later papers cite it

Evidence: substantial. 225 of the citing papers share no author with it, and 26 of those carry a confident label from Pith's citation classifier.

Pith read 24 of the 462 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

Uses its method or tool 1 of 5 papers with this label
How the literature uses it

168 arXiv papers cite this in 346 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 197 sentences without a confident label

Contests it 2 papers
  • Hence, in the case of Barrow holographic dark energy this recipe should be followed too (note that in [ref] it was tried to apply Barrow holographic dark energy in a non-flat universe but with $L$ being the Hubble horizon, a choice that is known to be not correct [ref] since it cannot lead to acceleration).

    Barrow Holographic Dark Energy in non-flat Universe · Barrow holographic dark energy in non-flat geometry · contest 0.74

  • This model was unable in order to obtain the standard HDE as a limit case, where the Hubble horizon as cutoff, provided an incorrect description when compared with case of the standard HDE [ref] .

    Cosmological perturbations in the Tsallis holographic dark energy scenarios · Introduction · contest 0.87

Builds on it 2 papers
  • I will then also expand on the model in [ref] , presenting more details about the time evolution in the context of an inflationary cosmology, and show that the addition of a simple physical principle can fix the ratio of the cosmological constant today to the one during inflation in terms of the number of e-folds of inflation.

    Quantum gravity and the holographic dark energy cosmology · Introduction · 1.00

  • We consider that each fundamental region is in its minimum energy state related with the Heisenberg uncertainty principle as well as the relation of the size of this regions with the Schwarzschild radius and the consideration of a relativistic behavior as an extension of the results obtained by several authors [ref] - [ref] .

    Dark Energy as a Geometric Behavior with Lower Dimensionality: A Toy Model · Introduction. · 0.96

Uses its method or tool 3 papers
Uses its data or values 1 paper
  • Finally, we note that it was shown in [ref] that a the exact solution for the evolution of the coupled system matter plus $Λ$ leads to an equation of state with w=-0.903+0.104z , since during pure $Λ$ domination, $ρ_Λ$ is truly constant (corresponding to $w=-1$), whereas during matter domination, $ρ_Λ∝1/a^2$, corresponding to $w=-1/3$ (in general, we have $ρ∝a^-3(1+w)$).

    Quantum gravity and the holographic dark energy cosmology · Holographic dark energy cosmology · 0.91

Compares with it 8 papers
Cites it as support 3 papers
Cites it as background 104 papers
  • Ricci dark energy, which is a kind of holographic dark energy [ref] taking the square root of the inverse Ricci scalar as its infrared cutoff, has been proposed by Gao et al. [ref] , and this model is also phenomenologically viable.

    Viscous Ricci Dark Energy · Introduction · 0.94

  • The holographic dark energy model [ref] [ref] is based on the simple idea that the vacuum energy density arising from the quantum fluctuation of the UV-cut-off quantum field theory should relate to the boundary surface of a system in the way ρ_Λ∼M_p^2L^-2, where $M_p^2=8πG$ is the reduced Planck mass, $L$ is the size of a system (thus $L^2$ is essentially the area of the boundary surface).

    An effective field theory of holographic dark energy · Introduction · 0.92

  • In the OHDE model [ref] , an accelerating expanding universe is achieved by choosing the future event horizon as the characteristic length, defined as [equation] where $a$ is the scale factor $a=(1+z)^-1$.

    Revisiting the Hubble tension problem in the framework of holographic dark energy · original holographic dark energy (OHDE) model · 0.95

Discussion

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