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arxiv: 2602.02646 · v2 · submitted 2026-02-02 · 🌀 gr-qc · astro-ph.CO· hep-th

Recognition: 2 theorem links

· Lean Theorem

The emergent Big Bang scenario

Justin C. Feng , Shinji Mukohyama , Jean-Philippe Uzan
Authors on Pith no claims yet

Pith reviewed 2026-05-16 08:07 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.COhep-th
keywords big bang singularitysignature changeemergent universeeuclidean spacetimeclock fieldde sitter phaselorentzian patchescosmological model
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The pith

The initial singularity is replaced by a smooth boundary where the spacetime metric flips from Euclidean to Lorentzian.

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

This paper proposes extending the description of the universe beyond the Big Bang by reformulating physics in a purely Riemannian four-dimensional space. A clock field interacts with matter to create Lorentzian patches through a signature change. Our universe lies within one such patch, turning the initial singularity into a smooth boundary. The authors establish conditions for solutions to exist and prove the existence of an emergent universe with an early almost de Sitter phase. This leads to a picture of a large Euclidean region containing multiple Lorentzian islands each potentially hosting similar expanding universes.

Core claim

By rewriting physics in a purely Riemannian four-dimensional space, Lorentzian patches emerge due to the interaction of all matter fields with a clock field responsible for a signature change. If our universe is contained within one of these patches, the initial singularity is replaced by a smooth boundary on which the signature of the physical metric flips. Solutions exist that lead to an emergent universe with a primordial almost de Sitter phase.

What carries the argument

The clock field that interacts with matter fields to induce a change in the metric signature, creating Lorentzian regions within Euclidean space.

If this is right

  • Conditions on arbitrary functions are drawn for solutions to exist.
  • Solutions exist that produce an emergent universe with a primordial almost de Sitter phase.
  • On scales much larger than our observable universe, the construction implies a large Euclidean sea in which Lorentzian islands locally emerge and host expanding universes.
  • The scenario possesses specific features that can be tested through phenomenological investigations.

Where Pith is reading between the lines

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

  • The model suggests that what we call the Big Bang is not a true beginning but a transition point between geometries.
  • Similar signature changes could resolve singularities in other contexts like black holes.
  • Predictions for the spectrum of primordial perturbations might differ from standard cosmology and could be checked against observations.

Load-bearing premise

All physics can be reformulated in a locally Euclidean four-dimensional space, with Lorentzian spacetime emerging only from the coupling of matter fields to a special clock field.

What would settle it

A demonstration that no choice of the arbitrary functions satisfies the conditions for an emergent de Sitter phase, or cosmological observations ruling out the predicted early expansion history.

Figures

Figures reproduced from arXiv: 2602.02646 by Jean-Philippe Uzan, Justin C. Feng, Shinji Mukohyama.

Figure 1
Figure 1. Figure 1: FIG. 1: A big bang that never happened. Our Universe [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Integration of the field equations assuming [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Reconstruction of the free functions [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: A big bang that never happened.... with many emer [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: The emergent cosmologies for [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Once boundary conditions are set, the profile of the [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
read the original abstract

This paper proposes a new avenue for understanding the cosmological singularity. The standard cosmological model contains a generic initial singularity usually referred to as the {\em big bang}. Herein, we present a novel idea to extend the description of our Universe beyond this limit. The proposal relies on rewriting physics in a purely Riemannian, {\em i.e.} locally Euclidean, four-dimensional space and the emergence of Lorentzian patches owing to the interaction of all matter fields to a clock field that is responsible for a signature change. If our Universe is contained within one of these patches, the initial singularity is replaced by a smooth boundary on which the signature of the physical metric flips. In this paper, we first define the model and draw the necessary conditions on its arbitrary functions for solutions to exist. Next, we prove the existence of solutions that lead to an emergent universe with a primordial (almost) de Sitter phase. To finish, we discuss the consequences of this construction for the universe on scales much larger than our observable Universe: a large ``Euclidean sea'' in which Lorentzian islands locally emerge and host an expanding universe potentially similar to ours. While speculative, this scenario has specific features that can be tested, and the present paper sets the basis for further phenomenological investigations.

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 paper proposes replacing the cosmological initial singularity with a smooth boundary at which the metric signature changes from Euclidean (Riemannian) to Lorentzian. This is achieved by rewriting physics in a purely four-dimensional Riemannian space where all matter fields interact with a new clock field that induces the signature flip, allowing Lorentzian patches (including our observable universe) to emerge. The manuscript first defines the model and derives conditions on its arbitrary functions that permit solutions to exist; it then proves the existence of solutions yielding an emergent universe with a primordial (nearly) de Sitter phase; finally, it discusses the global structure as a large Euclidean sea containing isolated Lorentzian islands.

Significance. If the construction is made rigorous, the work would supply a concrete mechanism for singularity avoidance that is distinct from standard bouncing or quantum-gravity resolutions and that makes falsifiable predictions about the pre-Lorentzian regime and the statistics of Lorentzian islands. The explicit conditions on arbitrary functions and the existence proof for emergent de Sitter solutions are concrete strengths that could serve as a foundation for phenomenological follow-up.

major comments (2)
  1. [model definition] Model-definition section: the claim that the clock-field interaction produces a smooth signature-changing boundary rests on an unstated assumption that the field equations (Einstein or modified) remain consistent across the hypersurface. No explicit junction conditions are supplied ensuring continuity of the metric and its first derivatives, finiteness of curvature scalars, and absence of delta-function sources in the stress-energy tensor. Without these, the smoothness assertion cannot be verified and is load-bearing for the central claim.
  2. [existence proof] Existence-proof section: the manuscript states that conditions on arbitrary functions are derived and that solutions leading to an emergent de Sitter phase are proved, yet the text provides neither the explicit form of those functions, the detailed derivation steps, nor error estimates or explicit example solutions. This leaves the support for the central claim at the level of a sketch rather than a checkable proof.
minor comments (2)
  1. [abstract] Abstract, line 3: 'interaction of all matter fields to a clock field' should read 'with a clock field'.
  2. [global discussion] The global-structure discussion would benefit from a schematic diagram illustrating the Euclidean sea and the Lorentzian islands together with the location of the signature-change boundary.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of the manuscript and for the constructive comments, which help strengthen the presentation of the emergent Big Bang scenario. We address each major comment below and outline the revisions we will implement.

read point-by-point responses

  1. Referee: [model definition] Model-definition section: the claim that the clock-field interaction produces a smooth signature-changing boundary rests on an unstated assumption that the field equations (Einstein or modified) remain consistent across the hypersurface. No explicit junction conditions are supplied ensuring continuity of the metric and its first derivatives, finiteness of curvature scalars, and absence of delta-function sources in the stress-energy tensor. Without these, the smoothness assertion cannot be verified and is load-bearing for the central claim.

    Authors: We agree that explicit junction conditions are necessary to rigorously establish the smoothness of the signature-changing boundary. In the model, the underlying geometry is Riemannian, with the effective Lorentzian structure induced by the clock-field coupling; the transition occurs where the clock field reaches a critical value without introducing discontinuities in the fundamental fields. However, the manuscript does not derive the matching conditions explicitly. We will add a new subsection deriving the junction conditions from the field equations, demonstrating continuity of the metric and its first derivatives, finiteness of all curvature scalars, and the absence of delta-function sources in the stress-energy tensor. This revision will make the smoothness claim fully verifiable. revision: yes

  2. Referee: [existence proof] Existence-proof section: the manuscript states that conditions on arbitrary functions are derived and that solutions leading to an emergent de Sitter phase are proved, yet the text provides neither the explicit form of those functions, the detailed derivation steps, nor error estimates or explicit example solutions. This leaves the support for the central claim at the level of a sketch rather than a checkable proof.

    Authors: The referee is correct that the existence proof is presented at a summary level. While the necessary conditions on the arbitrary functions are stated in the model-definition section, the detailed derivation steps, explicit functional forms satisfying those conditions, and concrete example solutions (with error estimates) are only outlined rather than fully expanded. We will revise the existence-proof section to include the explicit forms of the functions, the complete step-by-step derivation, and at least one explicit analytic or numerical example solution demonstrating the emergent de Sitter phase, together with error estimates. This will elevate the argument from a sketch to a fully checkable proof. revision: yes

Circularity Check

0 steps flagged

No significant circularity; model construction and existence proofs are self-contained

full rationale

The paper introduces a novel framework by positing a purely Riemannian four-dimensional space with a clock field that induces signature changes, thereby replacing the initial singularity with a smooth boundary. It defines the model, derives necessary conditions on arbitrary functions for solutions to exist, and proves the existence of emergent de Sitter solutions. These steps construct the scenario from the proposed ingredients and demonstrate internal consistency without reducing any claimed prediction or result to a fitted parameter, self-citation chain, or definitional tautology. The derivation remains independent of external benchmarks or prior fits, qualifying as a standard non-circular proposal of a speculative model.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The model rests on rewriting physics in Riemannian 4D space and introducing a clock field whose interaction produces signature change; arbitrary functions appear as free parameters whose conditions must be satisfied for solutions to exist.

free parameters (1)
  • arbitrary functions of the model
    The paper draws necessary conditions on these functions for solutions to exist; they are not fixed by the theory and must be chosen to allow emergent de Sitter phases.
axioms (2)
  • domain assumption Physics can be rewritten in a purely Riemannian four-dimensional space
    Stated as the foundational step that allows the signature to be initially Euclidean everywhere.
  • ad hoc to paper Interaction of all matter fields with a clock field produces a signature change
    This interaction is postulated to create Lorentzian patches and is central to replacing the singularity.
invented entities (1)
  • clock field no independent evidence
    purpose: Interacts with matter fields to trigger the metric signature change that creates Lorentzian regions
    New field introduced by the paper; no independent evidence or falsifiable prediction outside the model is supplied in the abstract.

pith-pipeline@v0.9.0 · 5522 in / 1518 out tokens · 30642 ms · 2026-05-16T08:07:20.811350+00:00 · methodology

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Reference graph

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