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arxiv: 2606.06282 · v1 · pith:DUFWWARInew · submitted 2026-06-04 · 🌀 gr-qc · hep-th

On Cosmological Correlators with Boundary Contributions

Yanjiao Ma , Dong-Gang Wang , Xiangwei Wang , Yi Wang , Wenqi Yu This is my paper

Pith reviewed 2026-06-28 00:11 UTC · model grok-4.3

classification 🌀 gr-qc hep-th
keywords cosmological correlatorsboundary termsfield redefinitionsmassive exchange diagramsde Sitter isometriesboost breakinginflationcosmological bootstrap
0
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The pith

Boundary terms in cosmological correlators correspond to field redefinitions and yield non-vanishing contributions under specific criteria.

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

The paper establishes a direct correspondence between boundary terms at the end of inflation and field redefinitions in the bulk Lagrangian for cosmological correlators. This correspondence supplies criteria that identify cases where boundary terms affect observables instead of being removable redundancies. The authors apply the result to massive-exchange diagrams both in de Sitter invariant theories and in boost-breaking theories. Integration by parts together with equations of motion reduce the diagrams, extract leading boundary pieces and infrared divergences, and produce recursion relations in the invariant case. In the broken case the same operations classify boundary contributions within the general effective field theory framework.

Core claim

Boundary terms correspond to field redefinitions for cosmological correlators. This provides criteria for when they lead to non-vanishing contributions. For dS-invariant theories, integration by parts and field redefinitions relate derivative and non-derivative exchange diagrams, from which leading boundary contributions and IR-divergent pieces are extracted and recursion relations among higher-derivative exchange correlators are derived. For boost-breaking theories, integration by parts and equations of motion reduce exchange diagrams to a basis of independent templates, and a classification of the boundary contributions is presented in the general effective field theory framework.

What carries the argument

The correspondence between boundary terms and field redefinitions, established through integration by parts and equations of motion, that determines when boundary terms contribute to cosmological observables.

If this is right

  • In dS-invariant theories the leading boundary contributions and IR-divergent pieces are extracted from massive-exchange diagrams.
  • Recursion relations connect higher-derivative exchange correlators.
  • In boost-breaking scenarios the diagrams reduce to a basis of independent templates.
  • Boundary contributions receive a classification inside the general effective field theory framework.

Where Pith is reading between the lines

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

  • The criteria may help isolate physical boundary effects when the same methods are applied to higher-point functions or loop diagrams.
  • If non-vanishing boundary terms survive, they could produce distinct signatures in primordial non-Gaussianity that differ from purely bulk contributions.
  • The reduction procedure might simplify analytic or numerical evaluations of correlators in a wider class of inflationary models.
  • The same logic could connect boundary physics to the treatment of surface terms in other gravitational effective theories.

Load-bearing premise

Integration by parts and field redefinitions can be applied to the massive-exchange diagrams without altering on-shell observables or introducing new physical content.

What would settle it

An explicit computation of a massive-exchange correlator performed once with the boundary term or field redefinition kept and once after the reduction, showing a mismatch in the final on-shell value, would falsify the claimed correspondence.

Figures

Figures reproduced from arXiv: 2606.06282 by Dong-Gang Wang, Wenqi Yu, Xiangwei Wang, Yanjiao Ma, Yi Wang.

Figure 1
Figure 1. Figure 1: Diagrammatic reduction rules, illustrated with the single-field example [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The diagrammatic triangle relating the three cases. [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The diagrammatic relation for the 3-pt correlator. The non-derivative exchange diagram is [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The diagrammatic relation for the 4-pt correlator. The late-time divergence of exchange diagram [PITH_FULL_IMAGE:figures/full_fig_p017_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Diagrammatic correspondence between the IBP and field redefinitions. The LHS depicts the [PITH_FULL_IMAGE:figures/full_fig_p021_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Diagrammatic rules for ghost fields. Arrowed lines denote ghost propagators, while purple dots [PITH_FULL_IMAGE:figures/full_fig_p033_6.png] view at source ↗
read the original abstract

Cosmological correlators receive contributions from both field interactions in the bulk of quasi-de Sitter (dS) spacetime and boundary terms at the end of inflation. While most of the research efforts focus on the former, boundary contributions are normally believed to be negligible or related to field redefinitions that are associated with redundancies of the bulk Lagrangian. In this paper, we revisit this topic in the light of the cosmological bootstrap. We first establish the correspondence between boundary terms and field redefinitions for cosmological correlators. This result provides a set of criteria for determining when boundary terms lead to non-vanishing contributions to cosmological observables. Next, we apply this general understanding to concrete examples of correlators from massive-exchange diagrams, in both dS-invariant and boost-breaking scenarios. For theories with dS isometries, both IBP and field redefinitions are used to relate derivative and non-derivative exchange diagrams, from which the leading boundary contributions and IR-divergent pieces are extracted; we also derive recursion relations among higher-derivative exchange correlators. For theories with broken dS boosts, we use IBP and EoM to reduce exchange diagrams to a basis of independent templates, and then present a classification of the boundary contributions in the general effective field theory framework. These results pave the way for a more systematic investigation on the boundary physics of the inflationary spacetime.

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

0 major / 3 minor

Summary. The paper claims to establish a correspondence between boundary terms at the end of inflation and field redefinitions (via integration by parts and equations of motion) for cosmological correlators in the bootstrap framework. This yields criteria for when boundary contributions are non-vanishing. The authors then apply the correspondence to massive-exchange diagrams, relating derivative and non-derivative exchanges in dS-invariant theories (extracting leading boundary and IR-divergent pieces plus recursion relations) and reducing diagrams to independent templates in boost-breaking EFTs with a classification of boundary contributions.

Significance. If the central correspondence and classification hold, the work supplies a systematic, bootstrap-compatible method for handling boundary redundancies in inflationary correlators. This is valuable for precision calculations in quasi-dS EFTs, as it converts potential boundary artifacts into bulk redefinitions and isolates genuine physical contributions, including IR pieces. The explicit recursion relations and template reduction in the two scenarios constitute concrete, reusable results that strengthen the bootstrap program for massive exchanges.

minor comments (3)
  1. The abstract states that IBP and field redefinitions 'relate' diagrams but does not specify the precise on-shell condition under which the correspondence preserves the correlator; a short clarifying sentence would help readers apply the criteria.
  2. In the dS-invariant section, the recursion relations among higher-derivative exchanges are presented without an explicit statement of the initial seed correlator used; adding this would make the relations immediately usable.
  3. Notation for the boundary operator and the IR-divergent pieces should be unified between the dS-invariant and boost-breaking sections to avoid minor confusion.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive and accurate summary of our work, which correctly identifies the central correspondence between boundary terms and field redefinitions, the criteria for non-vanishing contributions, and the concrete results on recursion relations and template reductions for massive-exchange diagrams. The recommendation for minor revision is noted. As the report lists no specific major comments, we have no points requiring point-by-point rebuttal or revision.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper derives a correspondence between boundary terms and field redefinitions using standard integration-by-parts and equations-of-motion identities applied to massive-exchange diagrams. These steps rely on general QFT redundancies rather than any fitted parameter renamed as a prediction, self-citation chain, or ansatz smuggled from prior work. The classification of boundary contributions in dS-invariant and boost-breaking cases follows directly from the stated IBP/EoM reductions without reducing the central claim to its own inputs by construction. The bootstrap framework is invoked as background context but does not bear the load of the new correspondence or criteria.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper rests on standard de Sitter isometries, the validity of integration by parts on the boundary, and the cosmological bootstrap framework; no new free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption De Sitter isometries and boost-breaking patterns allow consistent application of IBP and field redefinitions without changing on-shell physics
    Invoked when relating derivative and non-derivative exchange diagrams and when reducing to independent templates.
  • domain assumption Boundary terms at the end of inflation can be isolated after bulk interactions are accounted for
    Central to the correspondence claim in the abstract.

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discussion (0)

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Reference graph

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