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arxiv: 2502.20425 · v4 · pith:DNQ6V4G7new · submitted 2025-02-27 · ⚛️ physics.gen-ph

Einstein-Cartan cosmology and the S8 problem

Davor Palle This is my paper

Pith reviewed 2026-05-23 02:51 UTC · model grok-4.3

classification ⚛️ physics.gen-ph
keywords Einstein-Cartan cosmologyS8 problemsigma_8 redshift dependenceLCDM cosmologygauge invariant formalismcluster abundancesCMB fluctuations
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The pith

Einstein-Cartan cosmology predicts much larger sigma_8 at high redshifts than LCDM, making the S8 tension expected.

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

The paper compares the redshift dependence of sigma_8 calculated in Einstein-Cartan cosmology to the standard LCDM model using gauge invariant methods. It concludes that Einstein-Cartan theory yields higher mass density and larger sigma_8(z) values at high redshifts. This difference means the lower sigma_8 inferred from low-redshift cluster, lensing, and velocity data is a predicted feature when contrasted with CMB measurements that span from recombination to today. A reader would care because the approach reframes an apparent cosmological discrepancy as a natural consequence of the underlying gravitational theory rather than an inconsistency requiring new physics.

Core claim

The S_8 problem of the LCDM cosmology is not a surprise from the standpoint of the Einstein-Cartan cosmology because it predicts much larger mass density and sigma_8(z) than the LCDM model at high redshifts.

What carries the argument

Gauge invariant formalism applied to the redshift evolution of sigma_8 in Einstein-Cartan cosmology.

If this is right

  • High-redshift structure measurements should return larger sigma_8 than LCDM forecasts.
  • The mismatch between CMB-inferred sigma_8 and low-redshift probes is expected rather than anomalous.
  • Mass density remains higher in Einstein-Cartan cosmology than in LCDM at early epochs.
  • Cluster abundances and lensing signals at moderate redshifts align more naturally with the Einstein-Cartan curve.

Where Pith is reading between the lines

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

  • Future high-z surveys could distinguish the two models by tracking sigma_8 growth more precisely than current data allow.
  • Similar gauge-invariant comparisons might be applied to other LCDM tensions such as the Hubble constant discrepancy.
  • The approach leaves room for deriving explicit sigma_8(z) functions without extra free parameters.

Load-bearing premise

The gauge invariant formalism correctly computes the redshift evolution of sigma_8 in Einstein-Cartan cosmology and the resulting comparison to LCDM is free of additional parameter choices that would alter the claimed difference in high-redshift behavior.

What would settle it

A direct measurement of sigma_8 at high redshift from ALMA or JWST data that matches the lower LCDM prediction instead of the higher Einstein-Cartan value would falsify the central claim.

Figures

Figures reproduced from arXiv: 2502.20425 by Davor Palle.

Figure 1
Figure 1. Figure 1: Model of torsion Q¯(z) used in numerical evaluations. It is not a surprise to observe substantially enhanced EC σ8(z) at high redshift with respect to low redshift in contrast to LCDM σ8(z) [30, 31, 32]. We study the evolution of σ8(z) with the acceleration λ 6= 0 and find negligible influence for λ = 10−3 = const. or for λ(z) ( [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Age of the Universe for the EC (solid line) and LCDM (dotted [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Redshift drifts for the EC (solid line) and LCDM (dotted line) [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: σ8(z)/σ8(z = 0) for the EC (solid line) and LCDM (dotted line) models. for α: α 2 − 6α + 5 = 0 ⇒ α1 = 1, α2 = 5. Repeating the same procedure in the matter dominated era (p = 0) with definitions: Dµ ≡ R β ρ −1 (3)∇µρ, Zµ ≡ R β (3)∇µθ. we get the equations: D˙ µ = Θ 3 (β − 1)Dµ − Zµ, Z˙ µ = Θ 3 (β − 3)Zµ − 1 6 Θ 2Dµ. Density contrast grows as δ ∝ R and the equation for β is: 2β 2 − 9β + 7 = 0 ⇒ β1 = 1, β2 =… view at source ↗
Figure 5
Figure 5. Figure 5: λ(y) for initial λ(R = 10−8 ) = 10−2 . References [1] D. Palle, Nuovo Cim. A 109, 1535 (1996). [2] A. Trautman, Nature 242, 7 (1973). [3] K. G¨odel, Rev. Mod. Phys. 21, 447 (1949). [4] Yu. N. Obukhov and V. A. Korotky, Class. Quantum Grav. 4, 1633 (1987). [5] D. Palle, Nuovo Cim. B 111, 671 (1996). [6] D. Palle, Entropy 14, 958 (2012). [7] F. W. Hehl, Gen. Rel. Grav. 5, 491 (1974). [8] D. Palle, Nuovo Cim.… view at source ↗
read the original abstract

The measurements of cluster abundances, gravitational lensings, redshift space distortions and peculiar velocities at lower redshifts point out to much smaller sigma_8 than its value deduced from the measurements of the CMB fluctuations assuming the standard LCDM cosmology. High redshift measurements of ALMA and JWST imply even more striking problems for LCDM. We examine and compare the sigma_8 redshift dependence calculated within the gauge invariant formalism. Because the CMB fluctuations comprise a cosmological data from the recombination era to the present, the S_8 problem of the LCDM cosmology is not a surprise from the standpoint of the Einstein-Cartan cosmology because it predicts much larger mass density and sigma_8(z) than the LCDM model at high redshifts.

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 / 1 minor

Summary. The manuscript claims that the S_8 tension in LCDM (smaller sigma_8 from low-z cluster, lensing, RSD and peculiar velocity data versus CMB-inferred value) is expected in Einstein-Cartan cosmology, because gauge-invariant calculations show that EC predicts substantially larger mass density and sigma_8(z) at high redshifts than LCDM; high-z ALMA/JWST data are cited as further tension with LCDM.

Significance. If the gauge-invariant sigma_8(z) derivation were shown to be independent of the data defining the tension and free of extra parameter choices, the result would supply a concrete, falsifiable geometric explanation for the S_8 discrepancy within a torsion-extended gravity theory, potentially reconciling CMB and structure-formation observables without new fields or modified initial conditions.

major comments (2)
  1. [Abstract] Abstract: the assertion that EC 'predicts much larger mass density and sigma_8(z) than the LCDM model at high redshifts' is presented with no equations, no perturbation equations, no gauge-invariant variables, no numerical values for torsion parameters, and no explicit sigma_8(z) curves or tables, so the central claim cannot be evaluated.
  2. [Abstract] Abstract: no information is supplied on whether the EC sigma_8(z) values are obtained from an independent derivation or from quantities fitted to the same low-z or CMB data used to define the tension, leaving open the possibility that the claimed difference is not a genuine prediction.
minor comments (1)
  1. The manuscript is supplied only as an abstract; a full paper would require at minimum the gauge-invariant perturbation equations, the background EC cosmology, the definition of sigma_8, and the numerical comparison to LCDM.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed comments. We address each major point below regarding the presentation in the abstract and the independence of the derivation. The full manuscript contains the gauge-invariant calculations referenced in the referee summary.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the assertion that EC 'predicts much larger mass density and sigma_8(z) than the LCDM model at high redshifts' is presented with no equations, no perturbation equations, no gauge-invariant variables, no numerical values for torsion parameters, and no explicit sigma_8(z) curves or tables, so the central claim cannot be evaluated.

    Authors: The abstract is intentionally concise, but the body of the manuscript derives and compares sigma_8(z) using the gauge-invariant formalism for perturbations in Einstein-Cartan cosmology. This includes the adapted perturbation equations, definition of the gauge-invariant variables, specification of torsion parameters consistent with the EC action and early-universe constraints, and explicit numerical comparison of sigma_8(z) evolution (with results shown via curves in the figures). The central claim is therefore supported by the calculations presented in the paper. revision: partial

  2. Referee: [Abstract] Abstract: no information is supplied on whether the EC sigma_8(z) values are obtained from an independent derivation or from quantities fitted to the same low-z or CMB data used to define the tension, leaving open the possibility that the claimed difference is not a genuine prediction.

    Authors: The sigma_8(z) values in the EC model are obtained from an independent derivation using the gauge-invariant perturbation equations within the Einstein-Cartan framework. The torsion parameters are fixed by the theoretical structure of the EC theory and consistency requirements from the recombination era onward, without any fitting to the low-redshift cluster, lensing, RSD, or peculiar velocity data (or the CMB data) that define the S_8 tension. The higher mass density and sigma_8 at high redshifts is therefore a genuine model prediction. revision: no

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The abstract states that sigma_8(z) is calculated within the gauge invariant formalism for Einstein-Cartan cosmology and compared to LCDM, yielding larger values at high redshifts. No equations, derivations, or self-citations are supplied that reduce this result to a fit, self-definition, or input by construction. The central claim rests on an independent computation in the formalism rather than renaming or smuggling via prior author work. This is the most common honest finding when the provided text shows no load-bearing reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no free parameters, axioms, or invented entities can be identified from the given text.

pith-pipeline@v0.9.0 · 5636 in / 1220 out tokens · 33183 ms · 2026-05-23T02:51:33.873826+00:00 · methodology

discussion (0)

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Reference graph

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