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arxiv: 2606.27309 · v1 · pith:LJSNKMCUnew · submitted 2026-06-25 · ✦ hep-th · astro-ph.CO· gr-qc

Laplace Space for Cosmological Correlators

Nathan Belrhali , Arthur Poisson , S\'ebastien Renaux-Petel This is my paper

Pith reviewed 2026-06-26 02:21 UTC · model grok-4.3

classification ✦ hep-th astro-ph.COgr-qc
keywords cosmological correlatorsLaplace transformmassive single exchangeenergy singularitiesflat-space mappingintegral representationsearly universe theories
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The pith

A Laplace transform resolves each cosmological mode into a superposition of flat-space plane waves, allowing cosmological correlators to be computed via flat-space integrals against geometry-encoding kernels.

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

The paper shows that because cosmological modes oscillate like flat-space plane waves deep inside the horizon, a Laplace transform can represent them as dressed plane-wave superpositions whose kernels capture the effects of curved spacetime and field dynamics. This collapses the time integrals in correlator calculations to flat-space ones, yielding simple diagrammatic rules for turning cosmological diagrams into their flat-space versions integrated against the kernels. For the massive single exchange diagram, the representation makes energy singularities explicit and produces a single rapidly convergent series that works across the full kinematic domain without patching separate expansions. This matters because it offers a unified computational and conceptual tool for correlators in early-universe models.

Core claim

The Laplace transform provides an integral representation for cosmological modes that encodes the spacetime geometry, field content and dynamics in kernels, collapsing time integrals onto flat-space ones and supplying diagrammatic rules that map cosmological correlator diagrams to flat-space counterparts integrated against Laplace-space kernels. On the massive single exchange this yields a closed-form single rapidly convergent series valid throughout the kinematic domain that makes the energy singularities manifest.

What carries the argument

The Laplace transform that resolves each curved-space mode into a superposition of plane waves dressed by a kernel encoding the spacetime geometry, field content and dynamics.

If this is right

  • Cosmological correlator diagrams reduce to flat-space ones integrated against Laplace kernels.
  • Energy singularities appear manifestly in the integral representation for massive single exchange.
  • The result for massive single exchange is a single series valid in the entire kinematic domain without needing patched expansions.
  • The approach applies to virtually any theory of the early universe.

Where Pith is reading between the lines

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

  • This mapping could allow reuse of existing flat-space QFT techniques for cosmological calculations.
  • Similar transform methods might simplify computations in other spacetime backgrounds.
  • Explicit series forms could enable analytic studies of correlator properties like analytic continuation.

Load-bearing premise

Deep inside the horizon, every cosmological mode oscillates exactly as a flat-space plane wave.

What would settle it

A numerical evaluation of the massive single exchange correlator using the derived series in a kinematic regime previously requiring multiple expansions, compared against an independent method such as direct numerical integration of the time integrals.

Figures

Figures reproduced from arXiv: 2606.27309 by Arthur Poisson, Nathan Belrhali, S\'ebastien Renaux-Petel.

Figure 1
Figure 1. Figure 1: The single-exchange correlator s 2 ReF˜++ for µ = 2, rescaled by λu to expose the oscillatory cosmological collider signal on top of the smooth effective-field-theory background, along three slices of fixed ratio λv/λu. The curves are the master series truncated at total order 2n + m ≤ N = 8 (25 terms). Manifestly symmetric under λu ↔ λv, this single expansion covers the whole domain at once, including the… view at source ↗
read the original abstract

Deep inside the horizon, every cosmological mode oscillates as a flat-space plane wave. A Laplace transform turns this fact into a general method: it resolves each curved-space mode into a superposition of plane waves dressed by a kernel that encodes the spacetime geometry, field content and dynamics, collapsing the time integrals onto flat-space ones. This provides simple diagrammatic rules that turn cosmological correlator diagrams into their flat-space counterparts integrated against Laplace-space kernels. On the paradigmatic massive single exchange, this integral representation makes the energy singularities manifest and evaluates in closed form as a single, rapidly convergent series valid throughout the kinematic domain, with no patching of separate expansions. The Laplace approach sheds conceptual and computational light on cosmological correlators in virtually any theory of the early universe.

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 / 0 minor

Summary. The paper claims that a Laplace transform applied to cosmological modes (which oscillate exactly as flat-space plane waves deep inside the horizon) resolves each mode into a superposition of plane waves dressed by geometry/field kernels. This maps cosmological correlator diagrams to flat-space counterparts integrated against Laplace kernels, yielding simple diagrammatic rules. For the massive single-exchange diagram, the representation makes energy singularities manifest and evaluates to a single rapidly convergent series valid throughout the kinematic domain without patching separate expansions.

Significance. If the central construction holds, the method offers a unified computational framework for cosmological correlators that avoids regime-specific expansions and directly exposes singularities, with potential applicability across early-universe models. The claimed single-series evaluation for the paradigmatic diagram would be a concrete technical advance.

major comments (1)
  1. [Abstract] Abstract (opening sentence and central claim): the premise that 'deep inside the horizon, every cosmological mode oscillates as a flat-space plane wave' is used to collapse all time integrals onto exact flat-space ones and to obtain the claimed closed-form series. The manuscript provides no error estimate, regime of validity, or derivation showing that WKB/large-k corrections remain controlled and do not propagate into the energy singularities or series coefficients; this premise is load-bearing for the integral representation and the 'no patching' claim.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting this important point regarding the central premise. We respond to the major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract (opening sentence and central claim): the premise that 'deep inside the horizon, every cosmological mode oscillates as a flat-space plane wave' is used to collapse all time integrals onto exact flat-space ones and to obtain the claimed closed-form series. The manuscript provides no error estimate, regime of validity, or derivation showing that WKB/large-k corrections remain controlled and do not propagate into the energy singularities or series coefficients; this premise is load-bearing for the integral representation and the 'no patching' claim.

    Authors: We agree that the manuscript would be strengthened by an explicit derivation of the error estimates and regime of validity for the plane-wave approximation. The Laplace representation is constructed from the exact mode functions, with the flat-space identification entering through the leading WKB behavior at large k. We will add a dedicated appendix deriving the O(1/k) and higher WKB corrections, demonstrating that they are suppressed by the exponential decay of the Laplace kernel and do not shift the locations of the energy singularities or modify the coefficients of the convergent series. This will also make the domain of validity for the single-series representation fully explicit. revision: yes

Circularity Check

0 steps flagged

No circularity: Laplace method applies external premise to flat-space integrals

full rationale

The derivation begins from the stated physical premise that sub-horizon modes oscillate exactly as flat-space plane waves, applies the Laplace transform to produce kernels and diagrammatic rules, and obtains the single convergent series for the massive single-exchange diagram by integrating the resulting flat-space expressions. This premise is an input from cosmology rather than a result derived inside the paper; the output series and singularities are generated by the transform acting on external flat-space quantities. No self-definitional reduction, fitted parameter renamed as prediction, or load-bearing self-citation chain appears in the provided claims. The method remains self-contained against the external flat-space benchmark.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The method rests on the domain assumption that modes deep inside the horizon behave as flat-space plane waves; no free parameters or invented entities are mentioned in the abstract.

axioms (1)
  • domain assumption Deep inside the horizon, every cosmological mode oscillates as a flat-space plane wave.
    Opening premise of the abstract that enables the Laplace decomposition into plane-wave superpositions.

pith-pipeline@v0.9.1-grok · 5660 in / 1139 out tokens · 33252 ms · 2026-06-26T02:21:28.698478+00:00 · methodology

discussion (0)

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Reference graph

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