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arxiv: 2605.16869 · v1 · pith:VVEX5KL2new · submitted 2026-05-16 · 🌀 gr-qc · astro-ph.CO· hep-th

Gauge-invariant cosmological perturbations in Type 3 New General Relativity and background-hierarchy bounds

Kyosuke Tomonari , Daniel Blixt , Sebastian Bahamonde This is my paper

Pith reviewed 2026-05-19 20:57 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.COhep-th
keywords New General Relativitycosmological perturbationsgauge-invariant variablesbackground-hierarchy boundsFLRW backgroundType 3 NGRmodified gravity
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The pith

Type 3 New General Relativity permits consistent linear cosmological perturbations only within specific parameter bounds.

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

The paper derives background-hierarchy bounds for Type 3 New General Relativity, a modified gravity theory with two free parameters that preserves diffeomorphism invariance and spatial rotations but breaks Lorentz-boost invariance. These bounds arise by requiring that background spacetime evolution contributions exceed the quadratic kinetic terms in the perturbed Lagrangian around a flat FLRW universe. The analysis covers scalar, transverse-vector, and tensor modes and identifies the region of parameter space where linear perturbation theory stays viable for cosmological applications. A sympathetic reader cares because the bounds give a practical test for whether this theory can be applied to cosmic evolution without inconsistencies at linear order.

Core claim

We derive the background-hierarchy bounds for the scalar, transverse-vector, and tensor modes around a flat FLRW background, and identify the region of parameter space in which the linear perturbation theory of Type 3 remains viable for cosmological applications. The propagating modes are correctly identified even when the perturbed Lagrangian is not written solely in terms of gauge-invariant variables, after reviewing preferable gauge choices for metric-affine theories with Weitzenbock connection.

What carries the argument

Background-hierarchy bounds obtained by comparing background spacetime evolution contributions to quadratic kinetic terms in the perturbed Lagrangian.

If this is right

  • Linear perturbation theory of Type 3 remains viable for cosmological applications inside the derived parameter region for scalar, transverse-vector, and tensor modes.
  • Propagating modes stay correctly identified in the perturbative analysis without needing the Lagrangian written only in gauge-invariant variables.
  • Preferred gauge choices respect symmetries in both the Dirac-Bergmann analysis and linear perturbation theory for metric-affine theories with Weitzenbock connection.

Where Pith is reading between the lines

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

  • The derived bounds could be used to select parameter values when comparing Type 3 predictions to cosmic microwave background or large-scale structure data.
  • Similar hierarchy comparisons might apply to perturbation analyses in other New General Relativity types or teleparallel gravity models.
  • Violation of the bounds would require moving to nonlinear perturbation orders or including interaction terms to model the theory's behavior accurately.

Load-bearing premise

The bounds assume background spacetime evolution contributions always exceed quadratic kinetic terms from perturbations; if other higher-order or interaction terms become comparable at the same scale, the viability region no longer guarantees a consistent linear theory.

What would settle it

A concrete calculation showing the quadratic kinetic term dominating the background contribution for any mode inside the claimed viable parameter region would falsify the bounds.

Figures

Figures reproduced from arXiv: 2605.16869 by Daniel Blixt, Kyosuke Tomonari, Sebastian Bahamonde.

Figure 1
Figure 1. Figure 1: FIG. 1: Background-hierarchy bounds in Type 3 of NGR are shown in a single figure. All the bounds intersect at ( [PITH_FULL_IMAGE:figures/full_fig_p019_1.png] view at source ↗
read the original abstract

In this paper, we investigate background-hierarchy bounds in Type~3 of New General Relativity (NGR). These bounds arise when the contribution associated with the evolution of the background spacetime exceeds that of the quadratic kinetic term in the perturbed Lagrangian. Type~3 of NGR has two free parameters and preserves diffeomorphism invariance and spatial rotations, while breaking Lorentz-boost invariance. We first review Type~3 and identify preferable gauge choices for metric-affine gauge theories of gravity with Weitzenb\"ock connection, including NGR, from the viewpoint of symmetry in both Dirac--Bergmann analysis and linear perturbation theory. We then revisit the perturbative analysis of Type~3 and show that the propagating modes are correctly identified even when the perturbed Lagrangian is not written solely in terms of gauge-invariant variables. Finally, we derive the background-hierarchy bounds for the scalar, transverse-vector, and tensor modes around a flat FLRW background, and identify the region of parameter space in which the linear perturbation theory of Type~3 remains viable for cosmological applications.

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 paper reviews Type 3 New General Relativity, identifies suitable gauge choices for metric-affine theories with Weitzenböck connection, confirms that propagating modes (scalar, transverse-vector, tensor) are correctly identified in the linear perturbation analysis around flat FLRW even without exclusive use of gauge-invariant variables, and derives background-hierarchy bounds by requiring that the background spacetime evolution term exceeds the quadratic kinetic term in the perturbed Lagrangian. It then maps the resulting viable region in the two-parameter space for which linear cosmological perturbation theory remains applicable.

Significance. If the bounds hold and the linear truncation is self-consistent, the work supplies concrete parameter constraints that delineate where Type 3 NGR can be reliably used for cosmological applications. The explicit discussion of gauge choices and the demonstration that mode counting remains correct without full gauge-invariant reduction are useful technical contributions to the literature on metric-affine gravity.

major comments (1)
  1. The central viability claim rests on the background term dominating the quadratic kinetic term for each mode class. However, the manuscript does not supply an estimate showing that cubic or higher interaction terms remain parametrically smaller throughout the claimed region; if any such term becomes comparable near the boundary, the truncation to linear order would lose self-consistency. This assumption is load-bearing for the final statement that the identified parameter space supports reliable cosmological applications.
minor comments (1)
  1. The abstract and introduction would benefit from a brief statement of the explicit form of the two free parameters and the precise definition of the background-hierarchy ratio used to obtain the bounds.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive evaluation of the manuscript and for the constructive major comment. We address the point below and will revise the manuscript to strengthen the discussion of truncation self-consistency.

read point-by-point responses

  1. Referee: The central viability claim rests on the background term dominating the quadratic kinetic term for each mode class. However, the manuscript does not supply an estimate showing that cubic or higher interaction terms remain parametrically smaller throughout the claimed region; if any such term becomes comparable near the boundary, the truncation to linear order would lose self-consistency. This assumption is load-bearing for the final statement that the identified parameter space supports reliable cosmological applications.

    Authors: We agree that a complete justification of the linear truncation's validity would benefit from an explicit estimate of higher-order terms. The manuscript derives the background-hierarchy bounds by requiring that the background evolution term exceeds the quadratic kinetic contributions in the perturbed Lagrangian, thereby ensuring the linear equations remain a controlled approximation around flat FLRW. In the revised version we will add a short scaling argument in the discussion section (following the presentation of the bounds) showing that cubic interaction terms are suppressed by an additional factor of the dimensionless perturbation amplitude, which is assumed small (≪1) throughout the linear regime. Near the boundary of the viable parameter region this suppression factor remains intact, so the cubic terms stay parametrically smaller than the retained quadratic terms. A full nonlinear analysis lies beyond the present scope, which is limited to linear cosmological perturbations; we will note this limitation explicitly. We believe the added discussion will make the viability claim more robust without altering the central results. revision: yes

Circularity Check

0 steps flagged

No significant circularity; bounds derived by direct term comparison in perturbed Lagrangian

full rationale

The paper derives background-hierarchy bounds through explicit comparison of the background spacetime evolution term against the quadratic kinetic term in the perturbed Lagrangian for scalar, vector, and tensor modes around flat FLRW. This is a straightforward algebraic inequality obtained from the action expansion and does not reduce to any fitted parameter, self-referential definition, or load-bearing self-citation chain. Prior work on Type 3 NGR is reviewed for context and gauge choices, but the central viability region follows independently from the mode-by-mode term ordering without invoking uniqueness theorems or ansatze from the authors' own prior papers as the sole justification.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The analysis rests on the standard assumptions of linear cosmological perturbation theory and the symmetry properties that define Type 3 NGR; the two free parameters are inputs from the theory definition rather than new fitted quantities.

free parameters (1)
  • two free parameters of Type 3 NGR
    These parameters enter the action and are used to compute the bounds; they are part of the theory definition rather than fitted to the perturbation data.
axioms (2)
  • domain assumption Flat FLRW background spacetime
    Invoked when deriving the bounds for scalar, vector, and tensor modes.
  • domain assumption Preservation of diffeomorphism invariance and spatial rotations
    Stated as a defining property of Type 3 NGR used to select gauge choices.

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