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arxiv: 2606.27311 · v1 · pith:A4YQHOPSnew · submitted 2026-06-25 · ✦ hep-th · astro-ph.CO· gr-qc

Massive Cosmological Correlators from Flat Space: a Laplace-Space Approach

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

Pith reviewed 2026-06-26 02:18 UTC · model grok-4.3

classification ✦ hep-th astro-ph.COgr-qc
keywords cosmological correlatorsLaplace transformde Sittermassive exchangeenergy singularitiesmode functionsprimordial cosmology
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The pith

A Laplace transform of mode functions reduces cosmological correlators to flat-space calculations, giving a closed-form series for the massive single-exchange case.

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

The paper develops a Laplace-space approach to cosmological correlators based on the observation that modes oscillate as flat-space plane waves deep inside the Hubble radius. A Laplace transform expresses each mode as a superposition of plane waves with a kernel encoding the spacetime geometry. This turns time integrals into elementary flat-space integrals and provides diagrammatic rules. For the massive single-exchange correlator, the method makes energy singularities transparent and produces a single closed-form rapidly convergent series valid in the entire kinematic domain. The construction is claimed to apply essentially unchanged to many other situations in primordial cosmology.

Core claim

Representing each curved-space mode function as a continuous superposition of plane waves via Laplace transform, dressed by a kernel that encodes the spacetime geometry, field content and dynamics, reduces every time integral to an elementary flat-space one. Applied to the massive single-exchange correlator, this makes its total- and partial-energy singularities transparent from flat space and yields a single closed-form, rapidly convergent series valid throughout the entire kinematic domain.

What carries the argument

The Laplace representation of the mode functions, resolving curved-space modes into superpositions of flat-space plane waves dressed by a geometry-encoding kernel.

If this is right

  • Time integrals in correlators reduce to elementary flat-space integrals.
  • Diagrammatic rules emerge for computing cosmological correlators.
  • Total- and partial-energy singularities become transparent from flat space.
  • A single closed-form series converges rapidly for the massive single-exchange correlator across all kinematics.

Where Pith is reading between the lines

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

  • The method may extend directly to other types of correlators and field contents in de Sitter space.
  • Connections between curved-space cosmology and flat-space amplitudes could be explored further using this representation.
  • Testing the series convergence in extreme kinematic limits would confirm its utility.

Load-bearing premise

Deep inside the Hubble radius every mode oscillates exactly as a flat-space plane wave, with curvature effects entering only through the stretching toward the horizon.

What would settle it

A numerical evaluation of the massive single-exchange correlator in a kinematic regime where the proposed series diverges or fails to reproduce the expected singularities.

read the original abstract

We develop a new approach to cosmological correlators, built on a simple physical fact: deep inside the Hubble radius every mode oscillates as a flat-space plane wave, the curvature of spacetime making itself felt only as the mode is stretched towards the horizon. A Laplace transform turns this observation into a computational tool, resolving each curved-space mode function into a continuous superposition of plane waves labelled by a dual variable and dressed by a kernel that encodes the spacetime geometry, field content and dynamics. Every time integral then reduces to an elementary flat-space one, yielding simple diagrammatic rules for cosmological correlators. We illustrate the construction on the massive single-exchange correlator. The Laplace representation makes its total- and partial-energy singularities transparent ''from flat space'', and yields a single closed-form, rapidly convergent series valid throughout the entire kinematic domain. Although developed for conformally coupled fields exchanging massive scalars in de Sitter, the approach carries over essentially unchanged to virtually all situations of interest in primordial cosmology.

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 / 0 minor

Summary. The manuscript develops a Laplace-transform approach to cosmological correlators, based on the observation that modes deep inside the Hubble radius behave as flat-space plane waves with curvature effects entering only via stretching to the horizon. Mode functions are represented as continuous superpositions of plane waves dressed by a geometry- and dynamics-dependent kernel; time integrals then reduce to flat-space ones. The construction is illustrated explicitly for the massive single-exchange correlator of conformally coupled fields in de Sitter, producing a claimed closed-form, rapidly convergent series valid across the full kinematic domain that renders total- and partial-energy singularities transparent from flat space. The method is asserted to extend essentially unchanged to most situations of interest in primordial cosmology.

Significance. If the kernel is exact and the series converges uniformly, the approach supplies a concrete computational simplification for cosmological correlators by converting curved-space integrals into elementary flat-space ones without introducing free parameters or fitted quantities. The grounding in a standard Laplace transform and an external physical premise (rather than an ad-hoc ansatz) is a methodological strength, and the explicit illustration for the massive exchange diagram provides a falsifiable test case. Successful extension would be of broad utility for calculations that are otherwise obstructed by the de Sitter mode functions.

major comments (2)
  1. [Abstract] Abstract: the central claim that the Laplace transform supplies an exact representation of the curved-space mode functions (so that every time integral collapses to a flat-space integral without additional boundary terms or contour deformations) is load-bearing for the entire construction, yet the provided material contains no explicit derivation or verification that the kernel remains exact when the exchanged mass is nonzero.
  2. [Illustration on the massive single-exchange correlator] Illustration on the massive single-exchange correlator: the assertion of a single closed-form, rapidly convergent series valid throughout the entire kinematic domain (including near partial-energy singularities) requires explicit bounds or numerical checks on uniform convergence; without these the utility claim cannot be assessed.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address the two major points below and will incorporate clarifications and additional material in a revised version.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that the Laplace transform supplies an exact representation of the curved-space mode functions (so that every time integral collapses to a flat-space integral without additional boundary terms or contour deformations) is load-bearing for the entire construction, yet the provided material contains no explicit derivation or verification that the kernel remains exact when the exchanged mass is nonzero.

    Authors: The Laplace representation follows directly from the definition of the Laplace transform applied to the mode functions satisfying the linear mode equation; this holds for arbitrary mass without additional assumptions. We will add a dedicated subsection deriving the kernel explicitly for massive fields, confirming exactness by direct substitution into the mode equation and demonstrating that the transform properties eliminate boundary terms and contour issues, so that all time integrals reduce to flat-space ones by construction. revision: yes

  2. Referee: [Illustration on the massive single-exchange correlator] Illustration on the massive single-exchange correlator: the assertion of a single closed-form, rapidly convergent series valid throughout the entire kinematic domain (including near partial-energy singularities) requires explicit bounds or numerical checks on uniform convergence; without these the utility claim cannot be assessed.

    Authors: We agree that explicit verification of convergence is needed to support the utility claim. In the revision we will add numerical checks of truncation error for representative kinematic points across the full domain, including near partial-energy singularities, together with analytic bounds on the remainder derived from the large-argument decay of the kernel. These will be presented in an extended section on the single-exchange example. revision: yes

Circularity Check

0 steps flagged

Derivation self-contained from external physical premise and standard Laplace transform

full rationale

The paper grounds its method in an independent physical observation (flat-space plane-wave behavior of modes deep inside the Hubble radius) and applies the standard Laplace transform to obtain the kernel representation. No load-bearing step reduces the claimed series or diagrammatic rules to a fit, self-definition, or self-citation chain; the resulting closed-form expression for the massive single-exchange correlator is obtained by direct integration rather than by renaming or reparameterizing the target quantity itself. The construction therefore remains non-circular.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The approach rests on the standard de Sitter mode equation and the assumption that the Laplace kernel encodes geometry and dynamics without additional free parameters beyond those already present in the field content.

axioms (1)
  • domain assumption Deep inside the Hubble radius, every mode oscillates exactly as a flat-space plane wave.
    Invoked in the opening sentence of the abstract as the physical fact on which the Laplace transform is built.

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discussion (0)

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