Cosmological scenario based on the particle creation and holographic equipartition

Fei-Quan Tu; Qi-Hong Huang; Yi-Xin Chen

REVIEW 4 major objections 5 minor 54 references

Cosmological scenario based on the particle creation and holographic equipartition

T0 review · 4 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read This paper proposes that the whole expansion history—early inflation, radiation, present acceleration, and late de Sitter phase—can be produced by continuous particle creation under holographic equipartition, with no dark-energy component.

desk verdict A novel pairing of particle creation with holographic equipartition, but the printed de Sitter solution is dimensionally wrong and the transitions are unexplained, so the paper does not support its central narrative. read the letter →

arxiv 1908.11729 v1 pith:UKOVRLTU submitted 2019-08-30 gr-qc

Fei-Quan Tu , Yi-Xin Chen , Qi-Hong Huang This is my paper · ORCID

classification gr-qc

keywords particlecreationholographicequipartitiondarkenergyalternativeKomardeSitterexpansionacceleratinguniversecosmologicalthermodynamicspower-lawscalefactor

topics Dark Energy

open problems Dark Energy

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 proposes that a single thermodynamic idea can generate the whole expansion history of the universe without dark energy: the universe always creates particles, and the number of degrees of freedom inside the Hubble horizon always equals the number on the horizon (holographic equipartition). With radiation creation rate $\Gamma=\alpha H^2$ in the early universe, the solutions are an unstable de Sitter phase $a(t)\propto e^{\alpha t/3}$ followed by the standard radiation phase $a(t)\propto t^{1/2}$. With matter creation rate $\Gamma=\alpha H$ in the present and late universe, the solutions are accelerated power-law expansion $a(t)\propto t^\delta$ and a final de Sitter phase $a(t)\propto e^{Ht}$. Particle creation acts as an effective negative pressure, doing the work usually assigned to a cosmological constant. The paper also shows that the model preserves the thermodynamic relations $S=\frac{1}{2}\beta E$ and $dE=T\,dS$ on the Hubble horizon, while leaving the transition mechanisms between the regimes as open questions.

What carries the argument

The engine is the pair of evolution equations (20) and (21): the modified continuity equation $\dot{\rho}+3(1+\omega)H\rho\left(1-\frac{\alpha}{3}H^{n-1}\right)=0$, and the holographic-equipartition/Komar-energy relation $|\alpha(1+\omega)H^{n-1}-(1+3\omega)|\rho=\frac{3H^2}{4\pi L_p^2}$. These follow from the creation pressure $p_e=-(\rho+p)\Gamma/(3H)$ and the condition $N_{\text{bulk}}=N_{\text{sur}}$ with the Komar energy $\int(2T_{\mu\nu}-Tg_{\mu\nu})u^\mu u^\nu\,dV$ as the active gravitational energy. Combined with the power-law creation rate $\Gamma=\alpha H^n$ for $n=2$ in the early universe and $n=1$ in the present and late universe, these equations produce the four scale-factor solutions.

What would settle it

Fit the model's matter-era scale factor $a(t)\propto t^\delta$ to the observed distance-redshift relation of Type Ia supernovae over $0<z<1$: if a single, redshift-independent $\delta>1$ cannot accommodate the data, or if the required $\delta$ changes with redshift, the claim that one particle-creation regime explains present acceleration is refuted.

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Extended reading notes

Core claim

The central claim is that the equations of cosmology can be closed without a dark-energy term by combining the modified continuity equation for an open system with the holographic-equipartition condition $N_{\text{bulk}}=N_{\text{sur}}$, using the Komar energy as the active gravitational energy. The resulting evolution equation, $|\rho+3(p+p_e)|=3H^2/(4\pi L_p^2)$, together with the creation pressure $p_e=-(\rho+p)\Gamma/(3H)$, yields the scale factors. With $\Gamma=\alpha H^2$ and a radiation equation of state, the solutions split into a transient de Sitter stage $a\propto e^{\alpha t/3}$ and a radiation stage $a\propto t^{1/2}$; with $\Gamma=\alpha H$ and pressureless matter, they split into an accelerated power-law phase $a\propto t^\delta$ with $\delta>1$ when $1<\alpha<3$, and a late de Sitter phase $a\propto e^{Ht}$ when the creation rate reaches $\Gamma=3H$. The universe's evolution from inflation to late acceleration is thus recast as a sequence of particle-creation regimes, with no dark energy and no cosmological constant.

Load-bearing premise

The model assumes, rather than proves, that the universe keeps an exact balance between the number of microscopic degrees of freedom on its Hubble horizon and the number inside its volume at every moment; if that balance ever fails, the single evolution equation from which all the scale factors are derived has no basis.

Editorial extensions

If this is right

The accelerating phases of the universe are driven by the negative pressure created by particle production, so no cosmological constant or dark-energy field is required.
During matter domination, $\delta>1$ holds exactly when $1<\alpha<3$, and taking $\alpha=2$ gives $a(t)\propto t^2$, an expansion law the paper notes is consistent with supernova data.
When the creation rate reaches $\Gamma=3H$, the late universe becomes de Sitter, $a(t)\propto e^{Ht}$, independent of the matter equation of state.
In the early universe, $\Gamma=\alpha H^2$ with radiation gives an unstable de Sitter stage $a(t)\propto e^{\alpha t/3}$ that settles into the radiation era $a(t)\propto t^{1/2}$.
On the Hubble horizon the model preserves the equilibrium relations $S=\frac12\beta E$ and $dE=T\,dS$, so the assumed holographic equipartition is thermodynamically self-consistent.

Reading between the lines

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

Inference: The same pair of equations (20) and (21) is a template: other choices of $\Gamma\propto H^n$ can be tested against observed $H(z)$, so the framework is broader than the two worked-out cases.
Inference: The paper leaves the transitions between regimes—early de Sitter to radiation, and power-law to late de Sitter—without a mechanism; a dynamical rule for switching the creation rate would be the natural next step.
Inference: Because exact equipartition turns the horizon law into $dE=T\,dS$, the scenario treats the expansion as an equilibrium process on the Hubble horizon; computing the entropy production from particle creation would test whether that equilibrium picture is compatible with the irreversibility of particle creation.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Colleague,

The interesting thing here is the combination: Prigogine-style particle creation rates Γ=αH² (early) and Γ=αH (late) used with Padmanabhan's holographic equipartition as a single scenario. That specific pairing is not in the cited literature, and the paper shows how the equipartition condition plus the Komar energy leads to evolution equations that admit power-law and exponential solutions. The thermodynamic part—recovering S=½βE and dE=TdS inside the Hubble horizon—is consistent and done cleanly.

The problem is the central claim that these solutions form one continuous history. The paper itself concedes the transitions from e^{αt/3} to t^{1/2} and from t^δ to e^{Ht} are unclear. Worse, the early de Sitter solution as printed is wrong. Eq. (24) factors as (αH−3)(...) = 0, so the constant solution is H=3/α, not H=α/3. The abstract's a(t)∝e^{αt/3} cannot be recovered from their own equation. Since α has dimensions of time for Γ=αH², H=α/3 is dimensionally impossible. Fixing the typo to H=3/α saves the exponential solution but not the specific claim in the abstract.

There is also the parameter discontinuity: the power-law acceleration with ω=0 requires 1<α<3, while the subsequent de Sitter phase requires α=3. No dynamics connects these regimes, so the "whole evolution history" is an assembly of independent toy solutions with a hand-tuned α, not the output of one model.

What holds up: the algebra in Sections 4 and 5 is mostly correct, the thermodynamic consistency check is a real plus, and the authors are honest about the missing transitions. The idea is worth thinking about, but as written it does not deliver a coherent scenario.

I'd send it to a referee—it's the kind of paper where a reviewer can quickly identify the dimensional error and the patchwork issue, and the novel combination deserves a record. But it needs major revision before it could be accepted, and the abstract and conclusions would need to be rewritten.

Referee Report

4 major / 5 minor

Summary. The manuscript proposes a cosmological scenario based on two ingredients: particle creation in an open thermodynamic system and holographic equipartition. It assumes that the universe always satisfies N_bulk = N_sur (Eq. 7), uses the Komar energy as the active gravitational energy to derive the evolution equation (Eq. 16), and chooses a creation rate Gamma = alpha H^2 in the early radiation-dominated era (n = 2) and Gamma = alpha H in the present and late matter-dominated era (n = 1). From these choices the paper derives a de Sitter solution and a radiation solution for the early universe, and a power-law accelerated solution and a late de Sitter solution for the present and late universe, concluding that the whole evolution history can be explained without dark energy. It also derives the thermodynamic relations S = (1/2) beta E and dE = T dS for the Hubble horizon.

Significance. If the claimed scenario were valid, it would offer a genuinely dark-energy-free account of both early and late acceleration on the basis of thermodynamic ideas, and it would connect naturally to the Padmanabhan program of emergent gravity. The paper is clearly written and the algebraic structure of Eqs. (22)-(28) and the thermodynamic identities of Section 5 are transparent; the nonconstant solution (26) and the relation S = (1/2) beta E do follow from the stated equations. However, the central claim of a single coherent evolution history fails on internal grounds: the advertised early de Sitter solution is not a solution of the model's own equations, and the four regimes are presented as separate solutions with no dynamical connection. These are load-bearing problems, not presentation issues, and they undermine the main result.

major comments (4)

[Section 4.1, Eqs. (24)-(26)] The constant solution of Eq. (24) is H = 3/alpha, not H = alpha/3. Factoring Eq. (24) as (alpha H - 3)(-6H^3 + 4 alpha H^4 - 3 H dot H) = 0 shows that the constant solution is fixed by alpha H - 3 = 0. Moreover, with the creation rate Gamma = alpha H^2 from Eq. (19), alpha has dimensions of time, so H = alpha/3 is dimensionally inconsistent; H = 3/alpha is the dimensionally correct constant solution. Consequently Eq. (25), the abstract's a(t) proportional to e^{alpha t/3}, and the corresponding statements in the conclusions do not follow from the model's own equations; the correct de Sitter branch would be a(t) proportional to e^{3t/alpha}.
[Section 4.2 and Section 6] The claimed evolution history is an assembly of independent solutions, not one dynamical model. The accelerated power-law solution a(t) proportional to t^delta for omega = 0 requires 1 < alpha < 3, as follows from delta = 2/(3 - alpha) and delta > 1, while the subsequent de Sitter phase requires alpha = 3. The same parameter alpha of Eq. (19) would therefore have to change discontinuously at the transition, and no matching condition, transition mechanism, or dynamical rule is provided. The paper itself concedes in Section 6 that the transition mechanisms are unclear, which confirms that the four scale factors are not presented as part of a single solution. The central claim in the abstract and conclusions of a coherent evolution history is thus unsupported.
[Section 3, Eqs. (7), (14)-(16)] The fundamental evolution equation (16) is obtained by assuming exact holographic equipartition N_bulk = N_sur at all times, Eq. (7), and identifying the Komar expression in Eq. (14) as the relevant gravitational energy. All subsequent scale-factor solutions inherit this postulate, so the derived cosmological histories do not provide an independent test of the equipartition condition. The paper's language that the model 'explains' the acceleration without dark energy should be tempered by the fact that Eq. (7) is an input assumption whose validity through the radiation- and matter-dominated epochs is not examined. This is not an internal inconsistency, but it is a load-bearing condition that should be stated explicitly and discussed.
[Section 4.1, Eq. (23)] The derivation of Eq. (24) from Eq. (23) differentiates an equation containing an absolute value without tracking the sign. The argument 4 alpha H/3 - 2 changes sign at H = 3/(2 alpha), where the absolute value is non-differentiable, and the nonconstant solution (26) has two branches separated by this point. The paper does not specify which branch corresponds to the early universe or how the sign is chosen when deriving Eq. (24). A careful branch-by-branch derivation is needed if Eq. (24) is to be used globally.

minor comments (5)

[Section 3.2] The text contains a typo: 'Komor energy' should be 'Komar energy'.
[Sections 4.1 and 4.2] The same symbol alpha is used for two parameters with different physical dimensions: for n = 2, alpha has dimensions of time, while for n = 1 it is dimensionless. This should be stated explicitly to avoid confusion.
[Section 4.1, Eq. (26)] The statement that 'H = 1/(2t) when t is large' is only an asymptotic statement with logarithmic corrections, as can be seen from Eq. (26). The text should say so rather than implying exact equality.
[Section 4.2] The observational justification that a(t) = t^2 is consistent with supernova data is attributed to Ref. [47], which is a theoretical paper on scalar fields; a direct supernova data-analysis reference would be more appropriate.
[Abstract] The abstract's solution a(t) proportional to e^{alpha t/3} should be corrected in light of Major Comment 1, or the abstract should be rewritten to avoid the erroneous branch.

Circularity Check

1 steps flagged · score 2.0 of 10

Minor circular consistency argument in Sec. 5; the main scale-factor solutions are algebraic consequences of the paper's stated assumptions, not circular predictions.

self definitional [Section 5, paragraph after Eq. (32)]
"So the ansatz that the holographic equipartition is always satisfied throughout the evolution of the universe is consistent with the conclusion that the relation S = 1/2 βE is the energy equipartition in the static spacetime. In return, the validity of relation (32) also means that it is a reasonable ansatz that the universe obeys always the holographic equipartition."

Eq. (32), S = (1/2)βE, was derived earlier in the section from Eq. (10), E = 1/(H L_p^2), which itself came from imposing N_bulk = N_sur through Eqs. (8)-(9). The paper also states that S = (1/2)βE is 'indeed the energy equipartition law in the bulk when the holographic equipartition N_sur = N_bulk is satisfied.' Thus using the 'validity of relation (32)' to justify that N_bulk = N_sur is a reasonable ansatz is circular: the relation is a restatement of the equipartition assumption, not independent evidence for it. This is a minor consistency argument and is not needed for the scale-factor solutions in Sec. 4, which follow algebraically once the ansatz is assumed.

full rationale

The central derivation is not circular in the taxonomy sense: Eqs. (20)-(21) follow algebraically from the stated assumptions (particle creation with a chosen rate, the modified continuity equation, and the Komar-energy equipartition condition Eq. (16)), and the scale-factor solutions in Sec. 4 are obtained by solving those equations. The parameters α and δ are free model parameters rather than quantities secretly fitted and then renamed as predictions; the α = 2 example is an explicit match to observationally suggested a(t) = t^2, not an independent prediction claimed from first principles. The paper's holographic equipartition premise is cited to Padmanabhan's work, and the authors' own prior papers appear only in a survey list and are not load-bearing. The one genuine circular step is the Sec. 5 'in return' sentence, which uses S = (1/2)βE — itself equivalent to N_bulk = N_sur — to support that same ansatz; this does not affect the scale-factor derivation, so the score is low. Separately, but not as circularity: the claimed early de Sitter solution H = α/3 appears inconsistent with the paper's own Eq. (24), whose constant branch is H = 3/α, and the conclusion explicitly concedes that the transition mechanisms between the regimes are 'not clear.' Those are correctness and completeness limitations rather than circularity.

Assumptions & free parameters 2 free parameters · 9 assumptions · 0 invented entities

The model rests on the holographic equipartition postulate, the choice of Komar energy, and two hand-picked creation-rate laws; none of these are derived from first principles or independently constrained, which forces a high circularity burden.

free parameters (2)

alpha (early universe, from Gamma = alpha H^2) = not determined
Controls the de Sitter expansion rate a proportional to e^{alpha t/3} and the approach to radiation. No observational constraint is derived.
alpha (late universe, from Gamma = alpha H) = example alpha = 2 gives a(t) = t^2
For pressureless matter, acceleration requires 1 < alpha < 3. The example alpha = 2 is chosen to match a(t) = t^2 from Ref [47], a parameter selection rather than a predicted value.

assumptions (9)

domain assumption First law for an adiabatic open system with particle creation, d(rho V) + p dV = (h/n) d(nV), Eq. (2)
Adopted from Prigogine et al. [10]; assumes created particles are in equilibrium with the fluid.
domain assumption Particle number evolution equation n-dot + 3 H n = n Gamma
Standard in particle creation cosmology [10,33-35]; used without derivation.
ad hoc to paper Holographic equipartition N_bulk = N_sur holds at all times, Eq. (7)
Central postulate of the paper. The paper justifies it by reference to the holographic correspondence of the gravitational action, but does not derive it.
domain assumption Energy equipartition law E = (1/2) N_bulk k T, Eq. (6)
Taken from Padmanabhan's emergent gravity program [22,42].
domain assumption Surface degrees of freedom N_sur = A / L_p^2, Eq. (8)
Assumes a minimum quantum of area of order L_p^2 [42].
domain assumption Horizon temperature T = H / (2 pi)
Standard Gibbons-Hawking-like temperature for the Hubble horizon; used without derivation.
ad hoc to paper Komar energy is the active gravitational energy used in the equipartition law, Eq. (14)
The paper discusses both Misner-Sharp and Komar energies and chooses Komar because it is the active gravitational mass. This choice determines the form of Eq. (16); the Misner-Sharp choice would instead reproduce the standard Friedmann equation.
domain assumption The cosmic fluid has a constant equation of state p = omega rho, Eq. (17), with omega = 1/3 in the early era and omega = 0 in the present era
Standard cosmological assumption.
ad hoc to paper Particle creation rate Gamma = alpha H^n with n = 2 in the early universe and n = 1 in the present and late universe
The forms are chosen to produce the desired outcomes: high creation at early times and constant ratio Gamma/H at late times. The transition between n = 2 and n = 1 is not explained.

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Pith. "Pith review of Cosmological scenario based on the particle creation and holographic equipartition." pith.science (2026). https://pith.science/paper/UKOVRLTU

@misc{pith2026190811729,
  author       = {Pith},
  title        = {Pith review of: Cosmological scenario based on the particle creation and holographic equipartition},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UKOVRLTU}},
  note         = {Machine review of arXiv:1908.11729}
}

abstract

We propose a cosmological scenario which describes the evolution history of the universe based on the particle creation and holographic equipartition. The model attempts to solve the inflation of the early universe and the accelerated expansion of the present universe without introducing the dark energy from the perspective of thermodynamics. Throughout the evolution of the universe, we assume that the universe always creates particles in some way and holographic equipartition is always satisfied. Further, we choose that the creation rate of particles is proportional to $H^{2}$ in the early universe and to $H$ in the present and late universe, where $H$ is the Hubble parameter. Then we obtain the solutions $a(t)\propto e^{\alpha t/3}$ and $a(t)\propto t^{1/2}$ for the early universe and the solutions $a(t)\propto t^{\delta}$ and $a(t)\propto e^{Ht}$ for the present and late universe, where $\alpha$ and $\delta$ are the parameters. Finally, we obtain and analyze two important thermodynamic properties for the present model.

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