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arxiv: 2605.22143 · v1 · pith:XBQ67ZWZnew · submitted 2026-05-21 · 🌀 gr-qc · hep-th

Holographic Dark Energy with Hubble Radius as an Infrared Cutoff in Einstein-Cartan Gravity

Yongjun Yun , Jungjai Lee This is my paper

Pith reviewed 2026-05-22 05:52 UTC · model grok-4.3

classification 🌀 gr-qc hep-th
keywords holographic dark energyEinstein-Cartan gravitytorsion scalarHubble radiuscosmic accelerationphantom divideWeyssenhoff fluiddistance duality
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The pith

Torsion in Einstein-Cartan gravity shifts the equation of state of holographic dark energy to negative values, enabling cosmic acceleration.

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

The paper explores holographic dark energy with the Hubble radius as infrared cutoff in a theory that includes spacetime torsion. Using the Weyssenhoff spin fluid to describe the matter content, the torsion scalar is found to scale naturally as the inverse cube of the scale factor. This leads to a modification of the dark energy equation of state from dust-like to values that can approach minus one and cross the phantom divide even without interactions between dark matter and dark energy. The result provides a way to achieve cosmic acceleration and offers a dynamical model that may fit recent observations.

Core claim

By deriving the Einstein-Cartan equations and introducing a torsion scalar from a Weyssenhoff spin fluid, the model shows that in the absence of dark matter-dark energy interactions the torsion shifts the holographic dark energy equation of state toward negative values from the dust-like value in standard HDE. This allows the equation of state to approach ω_X ≃ -1 and cross the phantom divide in the weak torsion regime. The cosmic distance duality relation is modified accordingly while preserving the redshift-scale factor relation.

What carries the argument

The torsion scalar Φ scaling as Φ ∼ a^{-3}, derived directly from Einstein-Cartan field equations with Weyssenhoff spin fluid, which modifies the Friedmann-like equations and the dark energy equation of state.

If this is right

  • The equation of state for holographic dark energy becomes dynamical and can cross the phantom divide.
  • Cosmic acceleration is achieved without requiring interactions between dark sectors.
  • The model predicts gradual weakening of acceleration, potentially consistent with DESI observations.
  • The luminosity distance and angular diameter distance relation is modified by a torsion-dependent factor η.

Where Pith is reading between the lines

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

  • Resolving the need for ad hoc ansatz for torsion scaling could make such models more predictive.
  • Testing deviations in cosmic distance duality could provide evidence for torsion in the universe.
  • The weak torsion regime suggests compatibility with existing observational constraints on torsion.

Load-bearing premise

A Weyssenhoff spin fluid description suffices to derive the torsion scalar scaling directly from the Einstein-Cartan equations without additional assumptions.

What would settle it

Detection of a specific time-dependent deviation in the cosmic distance duality relation or an equation of state evolution that matches the predicted shift due to torsion but not standard models would support or refute the claim.

read the original abstract

In this work, we investigate non-interacting holographic dark energy (HDE) with the Hubble radius as the infrared cutoff in Einstein-Cartan gravity. We derive the Einstein-Cartan equations from the action principle and obtain Friedmann-like equations by introducing a torsion scalar. Considering a Weyssenhoff spin fluid, we determine the scaling behavior of the torsion scalar as $\Phi \sim a^{-3}$ without introducing an ad hoc ansatz, resolving the ansatz problem of previous torsion scalar scenarios. In the absence of interactions between dark matter and dark energy, the torsion scalar shifts the equation of state for holographic dark energy toward negative values from the dust-like value obtained in HDE without torsion, making cosmic acceleration possible. In particular, the resulting equation of state can approach $\omega_X \simeq -1$ and cross the phantom divide within the weak torsion regime $|\Phi/H| < 1$. The model predicts a dynamical equation of state in which cosmic acceleration gradually weakens, potentially consistent with recent DESI observations. In spacetimes with torsion, the cosmic distance duality relation between the luminosity distance $d_L$ and the angular diameter distance $d_A$ is modified as $d_L = d_A (1+z)^2 (1+\eta)$. In the presence of the torsion scalar, we show that the standard relation between redshift and the scale factor is preserved, while the deviation parameter arising from torsion effects is determined as $\eta \sim \int_{t_S}^{t_O} dt a^{-3}$, where $t_S$ and $t_O$ denote the emission time at the source and the observation time at the observer, respectively. Overall, our results support the feasibility of the model and provide a theoretical framework for preparing likelihood analyses.

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.

Referee Report

2 major / 2 minor

Summary. The manuscript investigates non-interacting holographic dark energy (HDE) with the Hubble radius as infrared cutoff in Einstein-Cartan gravity. It derives Friedmann-like equations incorporating a torsion scalar Φ, claims to obtain the scaling Φ ∼ a^{-3} from the Weyssenhoff spin fluid equations without ad hoc ansatz, and shows that this shifts the HDE equation of state ω_X from its dust-like GR value toward negative values, enabling cosmic acceleration and phantom divide crossing for |Φ/H| < 1. The model predicts a dynamical ω_X potentially consistent with DESI data and modifies the cosmic distance duality relation as d_L = d_A (1+z)^2 (1+η) with η ∼ ∫ dt a^{-3}.

Significance. If the derivation of the torsion scaling is free of implicit assumptions, the work supplies a field-equation-motivated resolution to the ansatz problem in torsion-extended HDE models and yields a concrete mechanism for acceleration without DM-DE coupling. The resulting dynamical equation of state and the modified distance-duality prediction constitute falsifiable outputs that could be confronted with current and forthcoming cosmological data.

major comments (2)
  1. [§3] §3 (derivation of torsion scalar from Weyssenhoff spin fluid): The central claim that Φ ∼ a^{-3} follows directly from the Einstein-Cartan field equations and the algebraic form of the spin tensor S^{μνλ} without additional ansatz requires explicit intermediate steps. In particular, the evolution or conservation law for the spin density in the FLRW background containing the holographic DE component must be shown; if this redshift law is inserted by hand or follows only after choosing the fluid equation of state, the asserted resolution of the ansatz problem is not secured and the subsequent ω_X shift rests on the same class of modeling choice it purports to avoid.
  2. [§4] §4 (equation-of-state analysis): The reported shift of ω_X from its dust-like value (ω_X = 0) to values approaching −1 and phantom crossing for |Φ/H| < 1 is load-bearing for the acceleration claim. This result is obtained by substituting the derived Φ scaling into the HDE continuity equation; therefore any residual assumption in the Φ scaling propagates directly into the viability of the acceleration and phantom-crossing statements.
minor comments (2)
  1. The integral expression for the deviation parameter η in the modified distance-duality relation would benefit from an explicit equation number and a brief discussion of its observational implications.
  2. Notation for the torsion scalar Φ and its relation to the spin density should be introduced with a dedicated equation to improve readability for readers unfamiliar with Einstein-Cartan literature.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. We address each major comment in detail below and will revise the paper accordingly to improve clarity and rigor.

read point-by-point responses

  1. Referee: [§3] §3 (derivation of torsion scalar from Weyssenhoff spin fluid): The central claim that Φ ∼ a^{-3} follows directly from the Einstein-Cartan field equations and the algebraic form of the spin tensor S^{μνλ} without additional ansatz requires explicit intermediate steps. In particular, the evolution or conservation law for the spin density in the FLRW background containing the holographic DE component must be shown; if this redshift law is inserted by hand or follows only after choosing the fluid equation of state, the asserted resolution of the ansatz problem is not secured and the subsequent ω_X shift rests on the same class of modeling choice it purports to avoid.

    Authors: We thank the referee for this important observation. In the revised manuscript we will expand the derivation in §3 with all intermediate steps. Starting from the Einstein-Cartan field equations with the algebraic spin tensor of the Weyssenhoff fluid, we project onto the FLRW background and obtain the conservation equation for the spin density. Because the spin fluid is non-interacting with the holographic dark energy, its continuity equation closes independently and yields ρ_s ∝ a^{-3} without reference to the DE equation of state. The torsion scalar is then related to this density by the standard EC relation Φ = (8πG/3)ρ_s (up to geometric factors), confirming the claimed scaling without an ad hoc ansatz. We will display these steps explicitly so that the independence from the DE component is transparent. revision: yes

  2. Referee: [§4] §4 (equation-of-state analysis): The reported shift of ω_X from its dust-like value (ω_X = 0) to values approaching −1 and phantom crossing for |Φ/H| < 1 is load-bearing for the acceleration claim. This result is obtained by substituting the derived Φ scaling into the HDE continuity equation; therefore any residual assumption in the Φ scaling propagates directly into the viability of the acceleration and phantom-crossing statements.

    Authors: We agree that the viability of the ω_X shift and the acceleration mechanism rests on the robustness of the Φ scaling. With the explicit derivation now provided in the revised §3, the substitution into the HDE continuity equation becomes fully justified. In the updated §4 we will show the algebraic steps that take Φ ∼ a^{-3} into the modified continuity equation, demonstrate the resulting dynamical ω_X that can approach −1 and cross the phantom divide for |Φ/H| < 1, and emphasize that no additional modeling choice for the DE fluid is required. This will make clear that the torsion-induced acceleration operates without DM-DE coupling. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation chain is self-contained

full rationale

The paper derives the torsion scalar scaling Φ ∼ a^{-3} by introducing a Weyssenhoff spin fluid into the Einstein-Cartan field equations and explicitly claims this avoids an ad hoc ansatz, resolving prior issues. The holographic dark energy equation of state is then shifted by this scaling in the non-interacting case to enable acceleration and phantom crossing for |Φ/H| < 1. This is a standard modeling sequence where the fluid description supplies the torsion behavior as input and the EOS modification follows as output. No self-definitional loop, fitted parameter renamed as prediction, or load-bearing self-citation chain is exhibited. The model remains self-contained against its stated assumptions and external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 3 axioms · 1 invented entities

The central claim rests on the Einstein-Cartan action, the Weyssenhoff spin-fluid ansatz for matter, the choice of Hubble radius as infrared cutoff, and the non-interacting assumption between dark sectors; these are standard or domain-specific inputs rather than new free parameters.

axioms (3)
  • standard math Einstein-Cartan gravity is obtained from the standard action principle with torsion
    Invoked to derive the modified Friedmann-like equations.
  • domain assumption Matter is described by a Weyssenhoff spin fluid
    Used to obtain the torsion scalar scaling Φ ∼ a^{-3}.
  • domain assumption Dark matter and dark energy do not interact
    Allows the torsion term to act alone on the dark-energy equation of state.
invented entities (1)
  • torsion scalar Φ no independent evidence
    purpose: Encodes the spin-torsion coupling in the cosmological equations
    Obtained from the Einstein-Cartan field equations with the spin fluid; no independent falsifiable prediction outside the model is given.

pith-pipeline@v0.9.0 · 5853 in / 1657 out tokens · 63621 ms · 2026-05-22T05:52:14.982472+00:00 · methodology

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