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arxiv: 2605.10548 · v1 · submitted 2026-05-11 · ✦ hep-th · gr-qc

Recognition: 1 theorem link

· Lean Theorem

Birth of Inflationary Universes via Wineglass Wormholes and their No-Boundary Relatives

George Lavrelashvili , Jean-Luc Lehners
Authors on Pith no claims yet

Pith reviewed 2026-05-12 04:44 UTC · model grok-4.3

classification ✦ hep-th gr-qc
keywords wormholesinflationary cosmologyno-boundary instantonsEuclidean gravityaxionic fieldstopology changeanalytic continuation
0
0 comments X

The pith

Wineglass wormholes can nucleate inflationary spacetimes from asymptotically flat or AdS regions via analytic continuation.

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

This paper examines Euclidean wineglass wormholes that connect to inflationary universes. These wormholes are distinguished by having a local maximum in the scale factor, which permits the continued Lorentzian geometry to expand after the tunneling event. Numerical solutions are constructed using either an axionic field or a magnetic gauge field, each paired with a self-interacting scalar field. When the charge is small, the wormhole geometry decomposes into the original background spacetime and an isolated no-boundary instanton. The work explores the details of this topology-changing transition and the shared properties of these instantons.

Core claim

Explicit numerical wormhole solutions supported by an axionic field or a magnetic gauge field, in conjunction with a self-interacting scalar field, demonstrate that wineglass wormholes mediate the nucleation of inflationary spacetimes from an existing spacetime with asymptotically flat or Anti-de Sitter regions. In the limit of small axionic or magnetic charge, these solutions split into two separate geometries consisting of the background spacetime and a disconnected no-boundary instanton.

What carries the argument

The wineglass wormhole geometry, identified by its local maximum of the scale factor that enables post-tunneling expansion in the Lorentzian continuation.

If this is right

  • These wormholes provide a mechanism for the birth of inflating universes from preexisting spacetimes.
  • More exotic solutions with multiple extrema of the scale factor can be constructed.
  • The topology changing transition links wineglass wormholes to no-boundary instantons.
  • The analytic continuation leads to expanding Lorentzian spacetimes after materialization.

Where Pith is reading between the lines

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

  • This suggests that no-boundary instantons may not be entirely disconnected but can emerge from modifications of wormhole geometries.
  • Such transitions might offer insights into how quantum effects allow topology change in gravity.
  • Further study could examine the stability of these solutions under perturbations.

Load-bearing premise

The analytic continuation from the Euclidean wineglass geometry to a Lorentzian expanding spacetime is valid and that the local maximum of the scale factor indeed triggers inflation after materialization.

What would settle it

A demonstration that the Lorentzian continuation from the scale factor maximum does not produce an inflating universe, or that no stable numerical solutions exist for the supporting fields, would falsify the proposed nucleation mechanism.

Figures

Figures reproduced from arXiv: 2605.10548 by George Lavrelashvili, Jean-Luc Lehners.

Figure 1
Figure 1. Figure 1: Euclidean wineglass wormholes describe the nucleation of an expanding universe (analytically [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: As the charge Q of the wineglass wormhole is reduced, the stem becomes thinner and thinner (left panel). In the limit of zero charge, a topological transition takes place: the stem pinches off, leaving behind a no-boundary instanton and a disconnected flat/AdS space (right panel). solution where the scalar field resides in the inflationary region from the part where the scalar reaches its asymptotic value.… view at source ↗
Figure 3
Figure 3. Figure 3: We will consider scalar potentials of sinusoidal form, parameterised such that the maxima are [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: An axionic wineglass wormhole with asymptotically flat boundary conditions. [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: A magnetic wineglass wormhole with asymptotically flat boundary conditions. [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Left: Initial scalar field values for the solutions listed in table I. Right: Sizes of the rim and stem for the same solutions. 9 [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Weightings of axionic and magnetic wineglass wormholes with asymptotically flat boundary [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: An axionic wineglass wormhole with asymptotically AdS boundary conditions. [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: “All roads lead to Rome.” Renormalized, background subtracted weightings of axionic [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: A wineglass wormhole with 2 stems, with Vmin = −1, Qa = 1, ϕ0 = 6.02621345, a0 = 1.96683280. Left: Evolution of the scale factor. Right: Evolution of the scalar field. Vmin=-1, Qa=1 0 2 4 6 8 10 12 τ 0.5 1.0 1.5 2.0 2.5 3.0 a(τ) Vmin=-1, Qa=1 valley top 2 4 6 8 10 12 τ -5 5 10 15 20 25 ϕ(τ) [PITH_FULL_IMAGE:figures/full_fig_p015_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: A wineglass wormhole with 2 stems, this time with the scalar interpolating across the potential barrier twice. Here Vmin = −1, Qa = 1, ϕ0 = 7.560478268, a0 = 2.168019383. Left: Evolution of the scale factor. Right: Evolution of the scalar field. each bounce of the scale factor – see [PITH_FULL_IMAGE:figures/full_fig_p015_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: A wineglass wormhole with 6 stems, with Vmin = −1, Qa = 1, ϕ0 = 7.4933858, a0 = 2.1571918. Left: Evolution of the scale factor. Right: Evolution of the scalar field. 15 [PITH_FULL_IMAGE:figures/full_fig_p015_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: The renormalized (but not background-subtracted) Euclidean action integrated from the [PITH_FULL_IMAGE:figures/full_fig_p016_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: A wineglass wormhole interpolating over two adjacent potential barriers. Here [PITH_FULL_IMAGE:figures/full_fig_p016_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Small-charge limit: A magnetic wineglass wormhole with asymptotically flat boundary [PITH_FULL_IMAGE:figures/full_fig_p017_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Friction term a/a, ˙ with the solid line corresponding to the numerical solution and the dashed line to the approximation in (18) respectively (21), for the axionic wormhole solution shown in [PITH_FULL_IMAGE:figures/full_fig_p018_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: The zero-charge limit of full wormholes. [PITH_FULL_IMAGE:figures/full_fig_p020_17.png] view at source ↗
read the original abstract

We study Euclidean wineglass wormholes, which mediate the nucleation of inflationary spacetimes from an existing spacetime with asymptotically flat or Anti-de Sitter regions. These wormholes are distinguished by the presence of a local maximum of the scale factor, which allows the analytically continued Lorentzian spacetime to expand after materialization. We present explicit numerical wormhole solutions supported either by an axionic field or a magnetic gauge field, in both cases in conjunction with a self-interacting scalar field. More exotic solutions, with multiple extrema of the scale factor, are also described. As we discovered recently, in the limit of small axionic or magnetic charge, wineglass wormhole solutions split into two separate geometries, one being the background spacetime and the other a disconnected no-boundary instanton. We study the associated topology changing transition in detail and provide an extensive discussion of both the properties and puzzles exhibited by this common family of wineglass/no-boundary instantons.

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 / 2 minor

Summary. The manuscript claims that Euclidean wineglass wormholes, distinguished by a local maximum in the scale factor, mediate the nucleation of inflationary Lorentzian spacetimes from asymptotically flat or AdS regions. It presents explicit numerical solutions for wormholes supported by an axionic field or a magnetic gauge field, each coupled to a self-interacting scalar field. In the small-charge limit these solutions split into a background spacetime plus a disconnected no-boundary instanton; the associated topology-changing transition is analyzed, along with more exotic multi-extrema solutions.

Significance. If the analytic continuation is shown to be consistent, the work would supply concrete numerical realizations of wormhole-mediated inflation nucleation and a topology-change mechanism linking to the no-boundary proposal. The explicit numerical constructions and the small-charge splitting constitute a technical contribution that could be used for further stability or semiclassical analyses in quantum cosmology.

major comments (1)
  1. [§4] §4 (analytic continuation and Lorentzian matching): the central claim that a local maximum of a(τ) in the Euclidean wineglass metric permits a valid Wick rotation to an expanding, inflationary Lorentzian geometry is load-bearing, yet the manuscript provides no explicit verification that the continued axion winding number or magnetic flux yields a stress-energy tensor satisfying the Lorentzian Einstein equations at the nucleation surface; without this check the splitting into a disconnected no-boundary instanton cannot be guaranteed to remain nonsingular or to produce inflation rather than recollapse.
minor comments (2)
  1. [§2] The metric ansatz for the wineglass deformation is introduced without an early, self-contained equation; adding an explicit line element in §2 would improve readability for readers outside the immediate subfield.
  2. [§3] Numerical convergence tests or residual errors for the axion and magnetic solutions are not tabulated; including a short table of shooting-parameter tolerances would strengthen the claim of 'explicit numerical solutions'.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for identifying the need for an explicit verification of the analytic continuation. We address this point directly below.

read point-by-point responses

  1. Referee: [§4] §4 (analytic continuation and Lorentzian matching): the central claim that a local maximum of a(τ) in the Euclidean wineglass metric permits a valid Wick rotation to an expanding, inflationary Lorentzian geometry is load-bearing, yet the manuscript provides no explicit verification that the continued axion winding number or magnetic flux yields a stress-energy tensor satisfying the Lorentzian Einstein equations at the nucleation surface; without this check the splitting into a disconnected no-boundary instanton cannot be guaranteed to remain nonsingular or to produce inflation rather than recollapse.

    Authors: We agree that an explicit check strengthens the central claim. The Euclidean equations are satisfied by construction, and the local maximum of a(τ) ensures that its first derivative vanishes at the nucleation surface, allowing a smooth Wick rotation to a Lorentzian geometry in which the scale factor has a minimum and subsequently expands. The axionic winding number and magnetic flux are continued analytically in the standard manner (the former becoming a time-dependent axion, the latter a magnetic field in the Lorentzian section). Nevertheless, the original manuscript did not include a direct substitution of these continued fields into the Lorentzian Einstein equations at the matching hypersurface. In the revised version we will add this verification in §4, confirming that the stress-energy tensor remains consistent, the geometry is nonsingular, and the subsequent evolution is inflationary rather than recollapsing. This addition will also make the small-charge splitting into a background spacetime plus a standard no-boundary instanton fully rigorous. revision: yes

Circularity Check

0 steps flagged

No significant circularity; numerical constructions are independent

full rationale

The paper's central results consist of new explicit numerical solutions to the Euclidean Einstein equations for wineglass wormholes, supported by axionic or magnetic gauge fields together with a self-interacting scalar. These are obtained by direct integration of the field equations rather than by fitting parameters to data subsets and then relabeling the outputs as predictions. The analytic continuation from the Euclidean metric (with its local scale-factor maximum) to a Lorentzian expanding spacetime is invoked as a standard procedure in instanton physics and is not derived from or equivalent to the solutions themselves by construction. The reference to a recent discovery of the small-charge splitting into background spacetime plus disconnected no-boundary instanton is a self-citation, but the present work independently computes the solutions and examines the topology change in detail; the main claims do not reduce to that prior reference. No self-definitional loops, smuggled ansatze, imported uniqueness theorems, or renaming of known empirical patterns occur. The derivation chain is therefore self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The work rests on the Euclidean path integral for gravity, the existence of analytic continuation to Lorentzian signature, and the validity of numerical solutions for the Einstein-scalar-axion or Einstein-scalar-gauge system. No new free parameters are introduced beyond standard field potentials and charges; no invented entities beyond the wormhole geometries themselves.

axioms (2)
  • domain assumption Euclidean Einstein equations with matter admit regular wormhole solutions that can be analytically continued to Lorentzian expanding cosmologies
    Invoked throughout the abstract to justify the nucleation interpretation
  • domain assumption The local maximum of the scale factor triggers post-materialization inflation
    Central to distinguishing wineglass wormholes from other instantons
invented entities (1)
  • wineglass wormhole no independent evidence
    purpose: Euclidean mediator for inflationary nucleation with local scale-factor maximum
    New geometry class introduced in the paper

pith-pipeline@v0.9.0 · 5465 in / 1436 out tokens · 24062 ms · 2026-05-12T04:44:42.633343+00:00 · methodology

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Reference graph

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