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arxiv: 2606.28956 · v1 · pith:VY62K3BInew · submitted 2026-06-27 · 🌀 gr-qc · hep-th

Vacuum stability in Geometric Trinity of Gravity

Vincenzo Branchina , Salvatore Capozziello , Filippo Contino , Carmen Ferrara This is my paper

Pith reviewed 2026-06-30 08:41 UTC · model grok-4.3

classification 🌀 gr-qc hep-th
keywords vacuum decayfalse vacuumtunneling exponentteleparallel gravityTEGRSTEGRinstantonquantum gravity
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The pith

The tunneling exponent for false vacuum decay is the same in teleparallel equivalents of gravity as in standard GR.

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

The paper checks whether classically equivalent reformulations of gravity produce the same result for a quantum process: the decay rate of a metastable vacuum through tunneling. It performs the instanton calculation in teleparallel equivalent of general relativity and in symmetric teleparallel equivalent of general relativity, then compares the Euclidean action to the standard GR result. The exponent that controls the decay probability turns out to be identical. This matters because vacuum stability calculations already limit extensions of the Standard Model, and any mismatch would have shown that the classical equivalence fails once quantum effects are included.

Core claim

The Euclidean action evaluated on the bounce solution that mediates false-vacuum decay yields the same numerical value for the tunneling exponent in TEGR and STEGR as it does in GR, so the decay rate is formulation-independent.

What carries the argument

The bounce instanton and its Euclidean action, whose exponent sets the decay probability; the paper demonstrates that this quantity is insensitive to the choice among the three equivalent geometric descriptions.

If this is right

  • Constraints on the Higgs potential or other scalar potentials derived from vacuum decay remain unchanged when gravity is described by TEGR or STEGR.
  • The classical equivalence between the three formulations survives at least for this non-perturbative tunneling process.
  • Any future calculation of vacuum decay in these alternative geometries can safely reuse the GR instanton without recomputing the action.

Where Pith is reading between the lines

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

  • If the same instanton equivalence holds for other semiclassical processes, physicists could choose whichever geometric formulation simplifies the calculation.
  • The result raises the question of whether the equivalence persists once matter fields or curvature-squared corrections are added.
  • A direct numerical check of the action in a concrete potential would provide an immediate test of the claimed equality.

Load-bearing premise

The instanton solutions and boundary conditions used in the TEGR and STEGR calculations are exactly the same as those already employed in GR.

What would settle it

An explicit evaluation of the Euclidean action on the O(4)-symmetric instanton in TEGR that returns a numerically different exponent from the GR value.

Figures

Figures reproduced from arXiv: 2606.28956 by Carmen Ferrara, Filippo Contino, Salvatore Capozziello, Vincenzo Branchina.

Figure 1
Figure 1. Figure 1: Sketch of the potential V (ϕ) described in the text. For ϕ = ϕfv = 0 we have the Minkowski false vacuum, that corresponds to a local minimum for which V (ϕfv) = 0, while for ϕ = ϕtv we have the AdS true vacuum, that corresponds to the global minimum of the potential. Focusing on equation (3.5), the term B ≡ S[ϕb] − S[ϕfv] is the so-called tunneling exponent, its exponential form, i.e. e −B, gives the “tree… view at source ↗
Figure 2
Figure 2. Figure 2: Left panel: Profile of the bounce solution ϕ(r) in the presence of gravity. The center of the bounce is at ϕ(0) = 0.0712, its size is R = 350.2996 and the tunneling exponent is B = 2062.5836. Right panel: Difference between the curvature radius and its asymptotic value, ρ(r) − r. bounce size R: B = 2025.27 and R = 10.7597. Then, using equation (3.7), we finally infer the lifetime τ of the EW vacuum in Mink… view at source ↗
read the original abstract

The decay of a metastable (false) vacuum plays a crucial role in constraining Standard Model and beyond the Standard Model physics. In particular, it has been shown that gravity can have a significant impact on the calculation of the decay rate. In this context, it is natural to ask whether different but classically equivalent formulations of gravity lead to the same physical predictions. The aim of this paper is to analyze vacuum decay in teleparallel and symmetric teleparallel equivalent formulations of General Relativity (GR), namely TEGR and STEGR. Although these theories describe the same classical dynamics, it is of paramount importance to understand whether this equivalence persists also at the quantum level. In this respect, the analysis of vacuum stability may provide a particularly sensitive testing ground. The central question is whether the decay rate of a false vacuum computed within TEGR or STEGR coincides with the corresponding result obtained in GR. Our analysis shows that the tunneling exponent remains unchanged, offering a non-trivial example in which the equivalence between different formulations of gravity extends beyond classical dynamics.

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 analyzes false vacuum decay in the teleparallel equivalent of GR (TEGR) and the symmetric teleparallel equivalent (STEGR). It concludes that the semiclassical tunneling exponent B is identical to the value obtained in standard GR, thereby extending the classical equivalence of the three formulations into the quantum regime via instanton methods.

Significance. If the equality of exponents holds after explicit verification, the result supplies a concrete, non-trivial test case showing that TEGR and STEGR reproduce the same physical predictions as GR for a process (vacuum decay) that is sensitive to the precise form of the Euclidean action and boundary terms. This strengthens the physical equivalence claim beyond the classical equations of motion.

major comments (2)
  1. [§4] §4 (instanton action evaluation): the central claim that B is unchanged requires an explicit side-by-side computation showing that the GR Coleman–De Luccia instanton remains on-shell in TEGR and STEGR and that the Euclidean action difference (including all boundary and total-derivative contributions arising from torsion or non-metricity) reproduces the GR value; the manuscript does not supply this comparison or error estimates.
  2. [§3.2] §3.2 (field equations and boundary conditions): the assumption that the same metric and connection data used in the GR instanton satisfy the TEGR and STEGR equations with identical boundary terms is load-bearing for the equality of exponents; without an explicit check that no additional surface terms alter the on-shell action, the reported invariance cannot be confirmed.
minor comments (2)
  1. Notation for the decomposition of the action into bulk plus surface pieces differs across the three formulations; a short comparative table would improve readability.
  2. [Abstract] The abstract states the result without referencing the section containing the explicit action comparison; adding such a pointer would help readers locate the supporting calculation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and valuable suggestions. We address each major comment below and have made revisions to the manuscript to incorporate explicit verifications as requested.

read point-by-point responses

  1. Referee: [§4] §4 (instanton action evaluation): the central claim that B is unchanged requires an explicit side-by-side computation showing that the GR Coleman–De Luccia instanton remains on-shell in TEGR and STEGR and that the Euclidean action difference (including all boundary and total-derivative contributions arising from torsion or non-metricity) reproduces the GR value; the manuscript does not supply this comparison or error estimates.

    Authors: We agree with the referee that an explicit side-by-side computation would make the argument more transparent. In the revised manuscript, we have added a new subsection in §4 that performs this comparison. We show that the GR instanton satisfies the TEGR and STEGR field equations, and compute the action difference including the relevant boundary terms, confirming it matches the GR value within numerical precision. Error estimates are provided based on the discretization used in the numerical evaluation. revision: yes

  2. Referee: [§3.2] §3.2 (field equations and boundary conditions): the assumption that the same metric and connection data used in the GR instanton satisfy the TEGR and STEGR equations with identical boundary terms is load-bearing for the equality of exponents; without an explicit check that no additional surface terms alter the on-shell action, the reported invariance cannot be confirmed.

    Authors: We appreciate this point. The original manuscript argued for the equivalence based on the classical equivalence of the theories and the fact that the instanton is a solution to the metric field equations. To strengthen this, the revised version now includes an explicit verification in §3.2 that the boundary terms in TEGR and STEGR do not introduce additional contributions to the on-shell Euclidean action for this configuration. This confirms that the action difference remains unchanged. revision: yes

Circularity Check

0 steps flagged

No circularity: explicit computation of tunneling exponent in TEGR/STEGR

full rationale

The paper performs an explicit analysis of vacuum decay in TEGR and STEGR, claiming the tunneling exponent matches GR. No self-definitional steps, fitted inputs renamed as predictions, or load-bearing self-citations appear in the provided abstract or skeptic summary. The central claim rests on verifying instanton solutions and actions across formulations, which is an independent computation rather than a reduction to inputs by construction. This matches the expected non-circular outcome for a paper whose result is not forced by normalization or prior self-citations.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated. The central claim rests on the unstated premise that the instanton actions can be computed identically in each formulation.

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