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arxiv: 2509.15317 · v2 · submitted 2025-09-18 · 🌀 gr-qc

On Scalar Cosmological Perturbations in Non-Minimally Coupled Weyl Connection Gravity

M. Lima , C. Gomes This is my paper

Pith reviewed 2026-05-18 15:34 UTC · model grok-4.3

classification 🌀 gr-qc
keywords scalar cosmological perturbationsWeyl connection gravitynon-metricity vectornon-minimal couplingblack hole solutionsdark matter mimicrycosmological field equations
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The pith

The non-metricity vector in this Weyl connection gravity model generates an extra force that mimics dark matter and dark energy while supporting Schwarzschild-like and Reissner-Nordström-like black hole solutions with an added horizon.

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

This paper examines scalar cosmological perturbations in a theory that couples matter non-minimally to curvature through a Weyl connection with non-metricity. The setup produces an extra force term from the non-metricity vector that can reproduce the observed effects of dark matter and dark energy while echoing Weyl's attempt to unify gravity and electromagnetism. The authors derive Schwarzschild-like and Reissner-Nordström-like black hole solutions that include an additional horizon caused by the non-metricity vector. They obtain the cosmological field equations under minimal coupling and present preliminary results on the evolution of scalar perturbations in this framework.

Core claim

In this non-minimally coupled Weyl connection gravity, the non-metricity vector supplies an extra force term that mimics dark matter and dark energy. The model admits Schwarzschild-like and Reissner-Nordström-like black hole solutions possessing an extra horizon due to non-metricity. Cosmological field equations are derived for the minimally coupled case, and initial results are given for scalar cosmological perturbations.

What carries the argument

The non-metricity vector of the Weyl connection, which supplies the extra force term in the gravitational field equations.

If this is right

  • Black hole solutions exhibit an extra horizon induced by the non-metricity vector.
  • The extra force term can account for dark-sector effects without separate dark matter or dark energy fields.
  • Scalar perturbation equations become available for direct comparison with cosmic microwave background and large-scale structure data.
  • The framework preserves Weyl's unification perspective between gravity and electromagnetism.

Where Pith is reading between the lines

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

  • The extra force may alter predictions for gravitational lensing or the propagation of gravitational waves around black holes.
  • Numerical integration of the perturbation equations could reveal distinct growth rates for cosmic structure compared with standard cosmology.
  • Parameter constraints from solar-system tests would directly limit the allowed strength of the non-metricity vector.

Load-bearing premise

The non-metricity vector can be tuned to generate a physically viable extra force that matches cosmological observations while remaining consistent with local tests of gravity.

What would settle it

Observation of an additional horizon around astrophysical black holes, or a scalar perturbation spectrum that deviates from standard predictions in a way that cannot be absorbed by adjusting the non-metricity strength.

read the original abstract

We analyze a theory with non-minimal matter-curvature coupling, considering non-metricity properties with a Weyl connection. This model has the advantage of an extra force term which can mimic dark matter and dark energy, and simultaneously follow Weyl's idea to unify gravity and electromagnetism. Indeed, Schwarzschild-like and Reissner-Nordstrom-like black hole solutions exist in this model, leading to new features, such as an additional horizon, due to the non-metricity vector. We derive the cosmological field equations, considering a minimal coupling, and discuss preliminary results on the scalar cosmological perturbations in this model.

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

1 major / 1 minor

Summary. The manuscript analyzes a gravitational theory with non-minimal matter-curvature coupling via a Weyl connection. This introduces a non-metricity vector that generates an extra force term claimed to mimic dark matter and dark energy while following Weyl's unification of gravity and electromagnetism. Schwarzschild-like and Reissner-Nordström-like black hole solutions are derived, featuring an additional horizon. Cosmological field equations are obtained under minimal coupling, with preliminary results presented on scalar cosmological perturbations.

Significance. If the non-metricity vector can be shown to reproduce observed cosmological expansion and structure growth without conflicting with local gravity tests, the model would offer a geometrically motivated alternative to dark sectors. The black hole solutions with extra horizons also suggest potential new phenomenology. However, the preliminary status of the perturbation analysis limits the current significance of the results.

major comments (1)
  1. [Cosmological field equations and scalar perturbations] Cosmological field equations and scalar perturbations section: the central claim that the extra force from the non-metricity vector can mimic dark matter and dark energy rests on an implicit assumption that its contribution can be parameterized to match the observed expansion history and structure growth while remaining consistent with solar-system constraints. No explicit matching to data, stability analysis, or bounds from local tests are provided to support this viability.
minor comments (1)
  1. [Abstract] The abstract refers to 'preliminary results' on perturbations without indicating the specific equations or key outcomes discussed in the text; adding a brief summary of the main findings would improve clarity.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback on our manuscript. We address the major comment below, acknowledging the preliminary character of the presented results while defending the scope of the current work.

read point-by-point responses

  1. Referee: [Cosmological field equations and scalar perturbations] Cosmological field equations and scalar perturbations section: the central claim that the extra force from the non-metricity vector can mimic dark matter and dark energy rests on an implicit assumption that its contribution can be parameterized to match the observed expansion history and structure growth while remaining consistent with solar-system constraints. No explicit matching to data, stability analysis, or bounds from local tests are provided to support this viability.

    Authors: We agree that the manuscript does not contain explicit observational fits, full stability analysis, or quantitative solar-system bounds. The central aim is to derive the cosmological field equations and the associated scalar perturbation equations in the presence of the non-metricity vector, showing how the extra force term arises naturally from the Weyl connection. The statement that this term “can mimic” dark sectors is therefore a statement about the structure of the equations rather than a claim of immediate phenomenological viability. We will revise the relevant section to (i) state the assumptions more explicitly, (ii) outline a possible parameterization of the non-metricity vector that could be confronted with data in future work, and (iii) add a short paragraph noting the necessity of future consistency checks with local gravity tests. These additions will make the scope and limitations of the present analysis clearer without altering the core derivations. revision: partial

Circularity Check

0 steps flagged

No circularity in derivation chain; model features follow directly from action and connection choice

full rationale

The paper starts from a non-minimally coupled action with Weyl connection, derives the field equations, obtains Schwarzschild-like and Reissner-Nordström-like solutions with an additional horizon from the non-metricity vector, and then computes the FLRW background plus scalar perturbation equations under minimal coupling. The extra force term is a direct geometric consequence of the chosen connection rather than a fitted parameter or output renamed as input. No load-bearing self-citations, ansatzes smuggled via prior work, or predictions that reduce to the same fitted quantities appear in the derivation steps. The analysis remains self-contained against the stated action and connection, with no reduction of claims to their own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The model rests on the standard Einstein-Hilbert action modified by a non-minimal coupling term and the definition of the Weyl connection; no new free parameters or invented entities are explicitly introduced in the abstract beyond the non-metricity vector already present in Weyl geometry.

axioms (2)
  • domain assumption The connection is a Weyl connection whose non-metricity is proportional to a vector field.
    Invoked when stating that the model follows Weyl's unification idea and produces an extra force term.
  • domain assumption The matter sector couples non-minimally to the curvature scalar.
    Stated as the central modeling choice that generates the extra force.

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Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

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supports
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extends
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Reference graph

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