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The adiabatic torsion mode of Einstein–Cartan cosmology cannot rescue Hubble-cutoff holographic dark energy: the holographic density cancels from the deceleration parameter, and the only acceleration is a bounce transient that a viable expa

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2026-08-01 21:41 UTC pith:SXXSCFZS

load-bearing objection Clean, honest no-go that kills the Hubble-cutoff HDE rescue by adiabatic EC torsion via a simple algebraic cancellation and a ladder of existence bounds, and it is entirely upfront that the result is conditional on adiabaticity.

arxiv 2607.16370 v1 pith:SXXSCFZS submitted 2026-07-17 gr-qc

No late-time role for adiabatic torsion: a no-go result for Hubble-cutoff holographic dark energy in Einstein--Cartan cosmology

Fernando Izaurieta , Samuel Lepe , Cristian Quinzacara This is my paper
classification gr-qc MSC 83F0583D05 PACS 98.80.-k
keywords Einstein–Cartan gravitytorsion cosmologyholographic dark energyHubble infrared cutoffdeceleration parametercosmological bounceDESI BAOadiabatic scaling
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.

This paper targets a recent proposal that spacetime torsion rescues the Hubble radius as the infrared cutoff for holographic dark energy, making it relevant to the DESI preference for evolving dark energy. The authors establish a no-go result: in Einstein–Cartan Friedmann cosmology, the homogeneous torsion mode compatible with a separately conserved matter sector must scale as a^{-3} and act as a stiff component of negative energy density. Under the Hubble cutoff, the holographic density is dynamically inert—it drops out of the deceleration parameter—so acceleration occurs only in the transient window between the torsion bounce and a scale factor 4^{1/3} times larger. Requiring that the universe have a past then bounds the torsion abundance at z=0 to at most 8.7e-4 from BAO data and as low as 5e-24 from Big Bang nucleosynthesis, leaving no late-time dark energy imprint. If correct, the paper redirects torsion cosmology away from adiabatic late-time mimicry toward mechanisms that break adiabaticity, such as spin alignment or propagating torsion.

Core claim

On the paper's own terms: in a flat Friedmann universe with Einstein–Cartan torsion and a separately conserved matter sector, the torsion scalar Phi satisfies Phi = Phi0 a^-3 and enters the Friedmann constraint as -3Phi0^2 a^-6, an effective stiff fluid of negative energy density. Adding the holographic density rho_hol = 3c^2 H^2, the deceleration parameter becomes q = (rho - 12Phi^2)/(2(rho - 3Phi^2)), independent of c^2: the holographic component merely renormalizes the constraint. Acceleration occurs if and only if rho < 12Phi^2, i.e. only for a_bar <= a < 4^{1/3} a_bar, the post-bounce transient. Placing that window at observable redshifts forces H^2=0 in our recent past. The resulting b

What carries the argument

The central object is the homogeneous axial torsion mode Phi(t) of Einstein–Cartan Friedmann cosmology. Adiabaticity—separate conservation of the matter sector—fixes its evolution to Phi ∝ a^-3, so it behaves as a stiff fluid with negative energy density, -3Phi^2 ∝ a^-6, and it generates the classical Einstein–Cartan bounce where H(a_bar)=0. The identity 6Phi(Phi_dot + 3HPhi) governs energy exchange between matter and torsion; setting it to zero is what makes the holographic density cancel from the deceleration parameter. This mode does the paper's work by confining all acceleration to the narrow window a_bar <= a < 4^{1/3} a_bar and by making the bound Omega_Phi < ~5e-24 follow from the mer

Load-bearing premise

The load-bearing premise is adiabaticity: the matter sector is separately conserved, which forces Phi ∝ a^-3 (constant spin per particle); if matter and torsion exchange energy, the torsion can dilute more slowly and the no-go result collapses.

What would settle it

Integrate Eqs. (1)–(2) numerically with separately conserved dust, Phi = Phi0 a^-3, and rho_hol = 3c^2 H^2, starting before the bounce; if q<0 is found at any a ≥ 4^{1/3} a_bar with H^2>0, the central cancellation claim is refuted. Observationally, a measurement requiring Omega_Phi above 8.7e-4 at 95% confidence—or an equation-of-state shift |1+w0| above 2 Omega_Phi/Omega_Lambda—would falsify the derived bound.

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

If this is right

  • With the Hubble cutoff, the holographic density is a spectator: it drops out of the deceleration parameter, so it cannot produce late-time acceleration or phantom crossing in this Einstein–Cartan model.
  • The only accelerating epoch is the bounce transient a_bar ≤ a < 4^{1/3} a_bar; shifting it to observed redshifts would mean H=0 in our recent past, which the measured expansion history excludes.
  • A viable cosmology bounds Omega_Phi = (Phi0/H0)^2 to 8.7e-4 (DESI DR2 BAO, 95% CL), 8.4e-5 (the z=14.32 galaxy), 3.1e-10 (CMB), and 5e-24 (BBN).
  • Today's equation-of-state imprint satisfies |1+w0| ≤ 2 Omega_Phi/Omega_Lambda, placing it between two and twenty-two orders of magnitude below the DESI DR2 preference and on the phantom side of -1.
  • For the Granda–Oliveros cutoff, torsion yields q<-1 identically and hastens the big rip instead of preventing it.

Where Pith is reading between the lines

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

  • Because the obstruction is pure background kinematics, the no-go is insensitive to whether DESI's preference for evolving dark energy survives future data; the bounce window is fixed by H^2≥0 alone.
  • The most promising loopholes are non-adiabatic torsion histories, where spin alignment or condensation keeps the torsion amplitude from diluting as a^-3, and dynamical (propagating) torsion modes, which the paper deliberately leaves untouched.
  • A natural observational extension is to use future high-z surveys to push the existence bound on Omega_Phi below 1e-24; conversely, a future data fit requiring Omega_Phi above 1e-3 would challenge the adiabatic scaling.

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

0 major / 3 minor

Summary. The paper claims a no-go result for Hubble-cutoff holographic dark energy in Einstein–Cartan cosmology with an adiabatic torsion mode. Starting from the modified Friedmann pair (1)–(2), the authors show that separate conservation of the matter sector forces the axial torsion scalar Φ to scale as a^{-3}, behaving as a stiff fluid with negative energy density. With the Hubble cutoff ρ_hol = 3c^2H^2, the holographic density cancels out of the deceleration parameter (Eq. 12), so any acceleration is only the EC bounce transient in the window \bar{a} ≤ a < 4^{1/3}\bar{a}. Requiring H^2>0 up to observed epochs gives nested bounds: Ω_Φ < 8.7×10^{-4} from DESI DR2 BAO, 8.4×10^{-5} from JADES-GS-z14-0 at z=14.32, 3.1×10^{-10} from the CMB, and 5×10^{-24} from BBN. The corresponding imprint on the dark-energy equation of state is |1+ω_0| ≤ 2Ω_Φ/Ω_Λ, far below and on the opposite side of the DESI preference. The Granda–Oliveros cutoff is also shown to deepen rather than avoid the big rip. Appendix A derives the Friedmann pair and traces the a^{-3} scaling to spin-fluid dilution.

Significance. If correct, the paper firmly refutes the recent claim in [11] that Einstein–Cartan torsion rescues the Hubble-radius holographic cutoff, and it shows that Hsu's tracker pathology persists in this extension. The central algebra is straightforward and I verified Eq. (12) by explicit differentiation of Eq. (11) with dust conservation and \dot{Φ}=-3HΦ; it reduces to q=1/2 in the torsionless limit. The expansion-history bounds are parameter-free consequences of H^2>0 and are easy to reproduce; the BBN bound at 5×10^{-24} is decisive if the adiabatic assumption holds. The paper is transparent about its scope: Sec. 6 and Appendix A explicitly identify adiabaticity as load-bearing and state that escaping the no-go requires matter–torsion energy exchange or late-time spin alignment. The DESI DR2 analysis uses the official likelihood, validates against ΛCDM, and finds no preference for torsion. These are genuine strengths; the paper does not overclaim.

minor comments (3)
  1. [Sec. 4, Eq. (17)] The bound is written with denominator (1+z)^6, but the exact consequence of H^2(z_max)>0 with flatness is Ω_Φ < [Ω_m(1+z)^3+Ω_r(1+z)^4+Ω_Λ]/[(1+z)^6-1] when Ω_Λ is the Ω_Φ-independent part. The difference is negligible at the redshifts considered (it changes the quoted bounds by less than 1 part in 10^4), but the formula as stated is not the strict logical consequence. Please correct the denominator or explicitly describe (17) as the asymptotic large-z form.
  2. [Sec. 3.1, Eq. (12)] The claim that differentiating Eq. (11) yields Eq. (12) is correct, but a two-line derivation would help readers who do not want to reconstruct the algebra. Consider adding an explicit intermediate step or an appendix note.
  3. [Sec. 5, Table 2 / text] The text says 'thirteen entries' with BGS D_V plus six (D_M,D_H) pairs, which is consistent. However, the table heading 'D_M/r_d, D_H/r_d' for the BGS row could be misread; only D_V/r_d is used there. A footnote clarifying the structure of the official DESI DR2 BAO likelihood would be helpful.

Circularity Check

0 steps flagged

No significant circularity: the no-go result is a conditional derivation with transparent assumptions, and the external DESI benchmark anchors the bounds.

full rationale

The paper's central claim is a scoped conditional: if the matter sector is separately conserved, then Phi ~ a^-3, the torsion mode acts as a negative stiff fluid, and the Hubble-cutoff holographic density drops out of the deceleration parameter. There is no circular step in this chain. Equations (1)-(2) are taken from Ref. [11], but Appendix A independently re-derives them from Einstein-Cartan field equations and the Weyssenhoff spin-fluid averaging, so the paper does not rely solely on a self-citation. The a^-3 scaling, Eq. (4), is a direct consequence of the stated adiabaticity assumption via the exchange identity (3); it is not a hidden import. The cancellation of rho_hol in Eq. (12) is an honest algebraic consequence of rho_hol = 3c^2H^2: differentiating the rescaled Friedmann constraint with dust conservation and Phi-dot = -3HPhi gives q = (rho - 12Phi^2)/(2(rho - 3Phi^2)), and the same result follows when the holographic pressure is fixed by its own conservation law. This is not a prediction forced by a fitted parameter; it is a mathematical identity that reproduces the known Hsu tracker pathology, which the paper explicitly credits. The expansion-history bounds in Eqs. (16)-(17) and Table 1 are parameter-free inequalities derived from requiring H^2 > 0 up to observed redshifts; the DESI DR2 BAO fit is a standard external-data constraint that validates the pipeline by reproducing the published LambdaCDM result exactly. Self-citations such as Refs. [20], [21], [23], and [25] are ancillary context (phantom asymptotics, spin-alignment speculation, gravitational-wave luminality) and are not load-bearing for the no-go. The paper also explicitly identifies its load-bearing assumption - adiabaticity - and discusses what breaking it would require. Thus the derivation is self-contained and the conditional claim is not circular.

Axiom & Free-Parameter Ledger

4 free parameters · 7 axioms · 0 invented entities

The central claim rests on: (i) the standard EC Friedmann pair for a homogeneous axial torsion mode, re-derived in Appendix A; (ii) adiabaticity forcing Φ∝a⁻³, explicitly flagged as load-bearing; (iii) the existence of observed early-universe epochs as boundary data; (iv) standard background parameters; (v) the standard treatment of the holographic component, validated by the torsionless Hsu limit; (vi) correct implementation of the DESI DR2 likelihood, validated by baseline reproduction. No invented entities; free parameters of the target model (c², α, β) cancel from the central result or are assumed in their usual regions.

free parameters (4)
  • Ω_m (adopted for existence bounds; also fitted in MCMC) = 0.3 (existence bounds); 0.312±0.013 (DESI fit)
    Standard prior value used to evaluate Eq. (17) for the JADES/CMB/BBN rungs; the rung values shift by roughly 30% for plausible Ω_m values, which does not affect the order-of-magnitude conclusions.
  • c² (Li's dimensionless holographic parameter) = unspecified (< 1)
    Parameter of the target model [11]. The central result is independent of its value: it cancels out of the deceleration parameter Eq. (12). No constraint on c² is needed for the no-go.
  • α, β (Granda–Oliveros cutoff parameters) = unspecified; assumes α<1, β>0
    Inputs from [16]. The conclusion that torsion deepens the big rip holds in this parameter region, which the paper calls 'the usual parameter region'. Other parameter regions are not analyzed.
  • H₀ r_d (drag-scale nuisance parameter in MCMC) = (100.8±0.9)×10² km/s
    Nuisance parameter marginalized in the DESI DR2 BAO fit; not load-bearing for the no-go argument. Reported for completeness and for the ΛCDM baseline validation.
axioms (7)
  • domain assumption The EC Friedmann pair Eqs. (1)–(2) correctly describe flat FLRW cosmology with a homogeneous axial torsion mode Φ, with Φ² identified with σ²/12 of the Weyssenhoff spin density.
    Starting point taken operationally from [11] Eqs. (3.28)–(3.29), and re-derived in Appendix A from EC field equations and spin-fluid averaging. The identification (A.3) carries literature normalization conventions.
  • domain assumption Matter is separately conserved (adiabaticity), which through the exchange identity (3) forces Φ̇ + 3HΦ = 0 and Φ ∝ a⁻³.
    Load-bearing assumption; Sec. 2, Eq. (4); explicitly flagged in Sec. 6. The paper states that breaking adiabaticity (interacting dark sector, spin alignment) evades the no-go.
  • domain assumption The expansion history extends to observed epochs: z=14.32 (JADES-GS-z14-0), z≈1090 (CMB), and 1+z≈4.3×10⁹ (BBN), i.e. H²(z)>0 there.
    Existence of spectroscopically confirmed objects and early-universe epochs; used to impose the bound Eq. (17). This is the 'universe must contain its own past' requirement.
  • domain assumption Standard flat ΛCDM budget with Ω_m=0.3, Ω_r=9.1×10⁻⁵ for the existence-bound rungs.
    Adopted from prior literature (Planck/DESI consistent values). Rung numbers shift by O(30%) for different Ω_m, but the multi-order-of-magnitude conclusions are insensitive.
  • domain assumption For the Hubble-cutoff holographic component, ρ_hol=3c²H², the constraint algebra with dust conservation and Φ̇=−3HΦ determines q; the result reduces to Hsu's tracker q=1/2 at Φ→0.
    Standard HDE treatment (Li 2004, Hsu 2004). Verified: differentiating Eq. (11) reproduces Eq. (12), and the torsionless limit matches the known result.
  • domain assumption The DESI DR2 BAO likelihood from the official release is correctly implemented in the MCMC (§5).
    Validated by reproducing the published DR2 ΛCDM fit within 0.0001 (Ωm=0.2976±0.0087 vs 0.2975±0.0086; H₀r_d=(101.54±0.74)×10² vs (101.54±0.73)×10²).
  • domain assumption Granda–Oliveros parameters lie in the region α<1, β>0.
    Quoted as 'the usual parameter region' from [16]; in this regime Eq. (13) gives q<−1 identically and torsion adds to super-acceleration.

pith-pipeline@v1.3.0-alltime-deepseek · 10640 in / 26068 out tokens · 243878 ms · 2026-08-01T21:41:55.682871+00:00 · methodology

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read the original abstract

In Friedmann cosmology with Einstein--Cartan torsion, the homogeneous torsion mode compatible with a separately conserved matter sector scales as $\Phi\propto a^{-3}$ and enters the Friedmann constraint as a stiff component of negative energy density, $-3\Phi^{2}\propto a^{-6}$. It has recently been claimed that this mode rescues the Hubble radius as an infrared cutoff for holographic dark energy, producing late-time acceleration and a phantom-divide crossing of possible relevance to DESI. We show that it cannot. With the Hubble cutoff the holographic density drops out of the deceleration parameter, and the only accelerating regime is the transient window $\bar{a}\leq a<4^{1/3}\bar{a}$ around the torsion bounce at $H(\bar{a})=0$; placing that window at observable redshifts would force the Hubble rate to vanish in our recent past, against the measured expansion history. Requiring a viable history yields nested upper bounds on $\Omega_{\Phi}\equiv(\Phi_{0}/H_{0})^{2}$: fitting the official DESI DR2 BAO likelihood gives $\Omega_{\Phi}<8.7\times10^{-4}$ ($95\%$ CL), the existence of a spectroscopically confirmed galaxy at $z=14.32$ gives $8.4\times10^{-5}$, the CMB gives $3.1\times10^{-10}$, and Big Bang nucleosynthesis gives $5\times10^{-24}$. Today's imprint on the dark energy equation of state, $|1+\omega_{0}|\leq2\Omega_{\Phi}/\Omega_{\Lambda}$, falls short of the DESI preference by two orders of magnitude at best and twenty-two at worst, and on the phantom side. In the Granda--Oliveros cutoff, torsion deepens rather than prevents the big-rip singularity. An appendix derives the Friedmann pair from the Einstein--Cartan field equations and shows that the $a^{-3}$ scaling is the kinematics of a diluting spin fluid; escaping the no-go requires breaking exactly that.

Figures

Figures reproduced from arXiv: 2607.16370 by Cristian Quinzacara, Fernando Izaurieta, Samuel Lepe.

Figure 1
Figure 1. Figure 1: The closing window. The curve is the maximum ΩΦ compatible with H2 (z) > 0 at each redshift, Eq. (17); the shaded region above it leaves no universe at that epoch. Markers show the ladder of [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Posterior from the DESI DR2 BAO fit of the flat ΛCDM+ΩΦ model. Left: 68% and 95% credible regions in the (Ωm, ΩΦ) plane. Right: marginalized posterior of ΩΦ with the one-sided 95% bound of Eq. (20). 6 Discussion: what it would take Every no-go is a list of assumptions read backwards, and ours has a short list. The load-bearing as￾sumption is adiabaticity. Everything hinges on Φ ∝ a −3 , which follows from … view at source ↗

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Reference graph

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