Non-interacting holographic dark energy with Torsion via Hubble Radius

Jungjai Lee; Yongjun Yun

arxiv: 2502.19880 · v2 · submitted 2025-02-27 · 🌀 gr-qc · astro-ph.CO· hep-th

Non-interacting holographic dark energy with Torsion via Hubble Radius

Yongjun Yun , Jungjai Lee This is my paper

Pith reviewed 2026-05-23 02:49 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.COhep-th

keywords holographic dark energytorsion scalarHubble radiuscosmic accelerationnon-interacting modelFriedmann cosmologyequation of stateinfrared cutoff

0 comments

The pith

Even weak torsion allows non-interacting holographic dark energy to use the Hubble radius as infrared cutoff and produce cosmic acceleration.

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

The paper reconstructs a holographic dark energy model inside a Friedmann cosmology that includes a torsion scalar, with no interaction between dark energy and dark matter. The Hubble radius is chosen as the infrared cutoff while the system is dominated by a time-dependent torsion scalar that arises from the spin of matter. In this setting, even very weak torsion produces accelerated expansion. The present-day equation-of-state parameter for the dark energy reaches a minimum value lying between just below -1 and -0.778 as a free parameter d runs from 1 to 0.654. The presence of torsion supplies a non-interacting limit that earlier models using the same cutoff lacked.

Core claim

Within a torsion-inclusive Friedmann cosmology and with no interaction between dark energy and dark matter, a holographic dark energy model that adopts the Hubble radius as infrared cutoff and is dominated by a time-dependent torsion scalar induced by matter spin yields cosmic acceleration even for arbitrarily weak torsion; the minima of the present equation-of-state parameter satisfy -1 < (ω_X^0)_min < -0.778 as d varies from 1 to 0.654, and the Hubble radius functions as a viable cutoff without requiring interaction.

What carries the argument

The time-dependent torsion scalar induced by matter spin, which dominates the system and modifies the Friedmann equations so that the Hubble radius can serve as infrared cutoff in a non-interacting holographic dark energy model.

If this is right

The model produces accelerated cosmic expansion without any interaction term between dark energy and dark matter.
The present equation-of-state minima lie in -1 < (ω_X^0)_min < -0.778 for d between 0.654 and 1.
The Hubble radius becomes a viable infrared cutoff for holographic dark energy once torsion is included.
For d approximately equal to 1 the equation-of-state behavior differs slightly from that of a cosmological constant.

Where Pith is reading between the lines

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

Torsion may remove the need for ad-hoc interaction terms in other holographic models that currently require them to make the Hubble radius work.
Late-time cosmological observations sensitive to the equation-of-state evolution could directly constrain the allowed range of the parameter d.
The same torsion mechanism might be examined in early-universe regimes where spin-torsion effects are stronger.

Load-bearing premise

The torsion scalar must be time-dependent, induced only by matter spin, and dominant enough that its specific functional form lets the Hubble radius act as the infrared cutoff while the model remains non-interacting.

What would settle it

A measurement showing that the present dark-energy equation-of-state parameter lies outside the interval -1 < ω_X^0 < -0.778, or an absence of late-time acceleration in a regime where torsion is weak but nonzero.

Figures

Figures reproduced from arXiv: 2502.19880 by Jungjai Lee, Yongjun Yun.

**Figure 2.** Figure 2: FIG. 2. Possible solutions of [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Close-up view of Fig. 2 for [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

read the original abstract

We reconstruct a holographic dark energy model within a Friedmann cosmology incorporating torsion scalar, assuming no interaction between dark energy and dark matter. Setting the Hubble radius as an infrared (IR) cut-off, we focus on a system dominated by contribution of a time-dependent torsion scalar induced by the spin of matter. In this regime, our results show that even very weak torsion causes cosmic acceleration. Specifically, we find that minima of the current equation of state for holographic dark energy, $(\omega_X^{0})_{min}$, lies in the range $-1 < (\omega_X^{0})_{min} < -0.778$ as a free parameter $d$ varies from $1$ to $0.654$. Focusing on the free parameter $d \approx 1$, we find that $(\omega_X^{0})_{min}$ exhibits slightly different behavior from the cosmological constant. Introducing torsion allows the Hubble radius to serve as a viable IR cut-off even without assuming the interaction between them. Moreover, this approach provides a non-interacting limit not found in earlier interacting models that use the Hubble radius as the IR cut-off.

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 fills the non-interacting holographic DE case with Hubble cutoff and torsion, but the torsion scalar form is inserted to close the system rather than derived.

read the letter

The main point is that this work reconstructs a non-interacting holographic dark energy model in torsion gravity, using the Hubble radius as IR cutoff, and shows that even weak torsion can produce acceleration with equation-of-state minima in -1 < (ω_X^0)_min < -0.778 as d runs from 1 to 0.654. The new element is the explicit non-interacting limit, which the abstract says was missing from earlier interacting Hubble-cutoff models. That gap-filling is the concrete addition. The reconstruction stays within the standard holographic-DE framework and simply adds the torsion scalar in a torsion-dominated regime induced by matter spin. On its own terms the algebra closes and yields the quoted range without needing an interaction term. That is useful for anyone already working in this corner of modified gravity. The soft spot is the torsion scalar itself. The abstract presents a time-dependent T(t) chosen so the Hubble cutoff works without interaction and produces the acceleration; there is no derivation shown from the Einstein-Cartan equations or from the evolution of spin density. If the actual torsion solution from the field equations differs, both the non-interacting condition and the numerical range for ω_X^0 fail. The parameter d is also free with no external anchor, so the minima are a scan rather than a fixed prediction. No data comparison or error propagation appears in the abstract. This is for readers already inside holographic dark energy plus torsion gravity who want the non-interacting extension. It does not reorganize the field or open new observational tests. A serious referee should check whether the torsion functional form is consistent with the modified Friedmann equations and whether the numerics hold once the derivation is written out. I would send it to peer review rather than desk-reject.

Referee Report

1 major / 2 minor

Summary. The paper reconstructs a non-interacting holographic dark energy model in Friedmann cosmology with torsion, using the Hubble radius as IR cut-off. It assumes a torsion-dominated regime with a time-dependent torsion scalar induced by matter spin, concluding that even weak torsion drives cosmic acceleration. Minima of the present equation-of-state parameter satisfy -1 < (ω_X^0)_min < -0.778 as free parameter d varies from 1 to 0.654; for d ≈ 1 the behavior differs slightly from a cosmological constant. The approach yields a non-interacting limit for the Hubble-radius cut-off not present in prior interacting models.

Significance. If the torsion scalar assumption is justified, the result is significant: it shows that torsion permits the Hubble radius as a viable IR cut-off without an interaction term, addressing a known limitation of earlier HDE reconstructions, and demonstrates that cosmic acceleration can arise from very small torsion contributions. The explicit numerical range for (ω_X^0)_min and the d ≈ 1 comparison to Λ provide concrete, falsifiable outputs within the model's parameter space.

major comments (1)

[Model reconstruction] Model reconstruction section: The specific functional form of the time-dependent torsion scalar T(t) (induced solely by matter spin in the torsion-dominated regime) is inserted to close the system and enforce the non-interacting condition with the Hubble-radius cut-off. No derivation from the Einstein-Cartan field equations, spin-density evolution, or modified Friedmann equations is supplied to establish that this T(t) is the consistent solution. Because the reported range -1 < (ω_X^0)_min < -0.778 and the claim that weak torsion suffices for acceleration both rest on this choice, the central results are conditional; an explicit consistency check or derivation is required.

minor comments (2)

[Abstract] Abstract: the free parameter d is introduced without definition or physical motivation; a brief statement of its origin (e.g., from the torsion ansatz or normalization) would improve readability.
[Results] Notation: the symbol (ω_X^0)_min is used repeatedly; a short table listing its value at the quoted d endpoints and at d ≈ 1 would make the parametric dependence clearer.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback on our manuscript. We address the single major comment point-by-point below. We agree that the torsion scalar form requires additional justification and will revise the manuscript to include a consistency discussion.

read point-by-point responses

Referee: [Model reconstruction] Model reconstruction section: The specific functional form of the time-dependent torsion scalar T(t) (induced solely by matter spin in the torsion-dominated regime) is inserted to close the system and enforce the non-interacting condition with the Hubble-radius cut-off. No derivation from the Einstein-Cartan field equations, spin-density evolution, or modified Friedmann equations is supplied to establish that this T(t) is the consistent solution. Because the reported range -1 < (ω_X^0)_min < -0.778 and the claim that weak torsion suffices for acceleration both rest on this choice, the central results are conditional; an explicit consistency check or derivation is required.

Authors: We acknowledge that the functional form of T(t) is introduced phenomenologically in the torsion-dominated regime to close the system under the non-interacting assumption with the Hubble-radius cutoff. This choice is motivated by the physical picture of torsion induced by matter spin, but we agree that no explicit derivation from the Einstein-Cartan equations or spin-density evolution is provided in the current manuscript. In the revised version we will add a short subsection clarifying the ansatz, showing its consistency with the modified Friedmann equations in the torsion-dominated limit, and including a brief consistency check. This will make the reported range for (ω_X^0)_min and the acceleration claim more robust while preserving the main conclusions. A full first-principles derivation from spin density would require further model assumptions on the matter sector and lies outside the present scope. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper reconstructs the holographic DE model by positing a time-dependent torsion scalar in a torsion-dominated regime (explicitly stated in the abstract) and then computes the resulting equation-of-state range while varying the free parameter d; this range is presented as the direct consequence of that variation rather than an independent prediction. No quoted equation reduces the central result to a self-definition, a fitted input renamed as prediction, or a load-bearing self-citation chain; the derivation remains self-contained once the stated ansatz and parameter are granted.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The model rests on the holographic principle with Hubble radius cutoff, the assumption of a time-dependent torsion scalar sourced by matter spin, and the standard Friedmann equations modified by torsion; d is introduced as a free parameter without independent calibration.

free parameters (1)

d
Free parameter varied from 1 to 0.654 to obtain the reported range of (ω_X^0)_min; no external constraint or derivation fixes its value.

axioms (2)

domain assumption Hubble radius serves as infrared cutoff for holographic dark energy density
Invoked to reconstruct the model; standard in holographic DE but here applied without interaction.
domain assumption Torsion scalar is time-dependent and induced by spin of matter in the dominant regime
Central modeling choice that supplies the acceleration without interaction.

invented entities (1)

time-dependent torsion scalar no independent evidence
purpose: Provides the extra degree of freedom that drives acceleration and permits non-interacting Hubble-radius cutoff
Introduced via the spin-torsion coupling; no independent falsifiable prediction (e.g., specific mass or coupling constant) is given in the abstract.

pith-pipeline@v0.9.0 · 5724 in / 1590 out tokens · 34658 ms · 2026-05-23T02:49:45.051913+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 propose the following ansatz within this framework: ϕ(t) ≃ −k H(t) (ρ_m(t) / (3 M_p² H₀²)) ... motivated by ... m=−1 and n=1
IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking contradicts

?

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

minima of the current equation of state ... −1 < (ω_X^0)_min < −0.778 as d varies from 1 to 0.654

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

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Holographic Dark Energy and Quantum Entanglement,

J. W. Lee, H. C. Kim and J. Lee, “Holographic Dark Energy and Quantum Entanglement,” J. Korean Phys. Soc. 74, 1–11 (2019)

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Holographic dark energy and cosmic coincidence,

D. Pavon, and W. Zimdahl, “Holographic dark energy and cosmic coincidence,” Phys. Lett. B 628, 206-210 (2005)

work page 2005

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Reconstructing Torsion Cosmology from Interacting Holographic Dark Energy Model,

S. Li, and Y. Chen, “Reconstructing Torsion Cosmology from Interacting Holographic Dark Energy Model,” Uni- verse. 9(2):100 (2023)

work page 2023

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Autoparallel vs. Geodesic Trajectories in a Model of Torsion Gravity,

L. Acedo, “Autoparallel vs. Geodesic Trajectories in a Model of Torsion Gravity,” Universe, 1(3), 422-445 (2015)

work page 2015

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Kine- matics of Einstein-Cartan universes,

K. Pasmatsiou, C. G. Tsagas, and J. D. Barrow, “Kine- matics of Einstein-Cartan universes,” Phys. Rev. D95, 104007 (2017)

work page 2017

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Friedmann-like universes with tor- sion,

D. Kranas et al., “Friedmann-like universes with tor- sion,” Eur. Phys. J. C 79:341 (2019)

work page 2019

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Methods for deriving solutions in gener- alized theories of gravitation: The Einstein-Cartan the- ory,

M. Tsamparlis, “Methods for deriving solutions in gener- alized theories of gravitation: The Einstein-Cartan the- ory,” Phys. Rev. D24, 1451 (1981)

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Gao S. “Explaining Holographic Dark Energy,” Galaxies. 1(3):180-191 (2013)

work page 2013

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J. W. Lee, J. Lee, and H. C. Kim, “Dark energy from vacuum entanglement,” JCAP 0708:005 (2007)

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Q. G. Huang, and M. Li, “The Holographic dark energy in a non-flat universe,” JCAP 08 013 (2004)

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Adam G. Riess et al., “A comprehensive measurement of the local value of the Hubble constant with 1 km s −1 Mpc−1 uncertainty from the Hubble Space Telescope and the SH0ES team,” ApJL934L7 (2022)

work page 2022

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S. H. Pereira et al., “Acceleration in Friedmann cosmol- ogy with torsion,” Eur. Phys. J. C 79:950 (2019)

work page 2019

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Big bang Nucleosynthesis: Present status,

R.H. Cyburt, B.D. Fields, K.A. Olive, and T.-H. Yeh, “Big bang Nucleosynthesis: Present status,” Rev. Mod. Phys.88, 015004 (2016)

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work page 2018