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arxiv: 2605.19331 · v1 · pith:TL3RHOBNnew · submitted 2026-05-19 · 🌀 gr-qc · astro-ph.CO· hep-th

Locality in effective field theory for inflationary soft modes

Takahiro Tanaka , Yuko Urakawa This is my paper

Pith reviewed 2026-05-20 05:16 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.COhep-th
keywords inflationary cosmologysoft modeseffective field theorygradient expansionsoft theoremsinfrared divergenceslocality conditionconsistency relations
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The pith

A locality condition on hard-mode states unifies the effective description of inflationary soft modes with soft theorems and IR regularity.

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

The paper establishes that a quantum state satisfies a locality condition when the hard-mode configuration inside each local patch depends on the soft modes only through the local values of those soft modes inside the same patch. When this holds, the coarse-grained dynamics of the soft modes stays local after integrating out shorter wavelengths. The same condition suppresses perturbative loop corrections from hard modes to superhorizon correlators of the curvature perturbation and guarantees infrared regularity for operators that are invariant under large gauge transformations. It also yields a generalized soft theorem from which the usual consistency relations follow once extra assumptions are added. A sympathetic reader cares because the condition supplies a model-independent test for when the gradient expansion and separate-universe picture remain reliable even in multi-field or non-attractor settings.

Core claim

When the hard-mode state in each local universe depends on the soft modes only through the local soft-mode values in the same patch, the coarse-grained soft-mode dynamics remains local, loop corrections from hard modes to superhorizon correlators of the adiabatic curvature perturbation are perturbatively suppressed, a generalized soft theorem holds, and correlators of operators invariant under a large gauge transformation remain free of infrared divergences. This supplies a unified criterion that diagnoses when enhanced hard-mode corrections can invalidate the gradient expansion and clarifies the origin of possible deviations from standard consistency relations.

What carries the argument

The locality condition that the hard-mode state inside each patch depends on soft modes solely through the local soft-mode values inside that patch.

If this is right

  • Coarse-grained soft-mode dynamics remains local after integrating out hard modes.
  • Perturbative loop corrections from hard modes to superhorizon correlators are suppressed.
  • A generalized soft theorem holds, from which standard consistency relations follow under additional assumptions.
  • Correlators of operators invariant under large gauge transformations are free of infrared divergences.

Where Pith is reading between the lines

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

  • The criterion could be checked directly in lattice simulations by verifying whether subhorizon mode amplitudes depend only on the local superhorizon background inside each patch.
  • Models that violate the condition may produce observable departures from consistency relations without requiring new light degrees of freedom.
  • The same locality requirement might apply to soft-mode descriptions in other expanding cosmologies where a gradient expansion is used.

Load-bearing premise

A quantum state obeying the locality condition can be consistently defined and preserved by the inflationary dynamics.

What would settle it

An explicit construction or numerical simulation of an inflationary state in which the hard-mode configuration in a patch depends on non-local soft-mode information, followed by the appearance of unsuppressed hard-mode loop corrections or infrared divergences in gauge-invariant correlators, would falsify the central claim.

Figures

Figures reproduced from arXiv: 2605.19331 by Takahiro Tanaka, Yuko Urakawa.

Figure 1
Figure 1. Figure 1: Schematic illustration of the locality condition. After dividing the spatial slice into local patches [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
read the original abstract

The gradient expansion and the separate universe approach provide an effective description of inflationary soft modes after coarse-graining shorter-wavelength degrees of freedom. We formulate a locality condition on the quantum state, requiring that the hard-mode state in each local universe depend on the soft modes only through the local soft-mode values in the same patch. When this condition is satisfied, the coarse-grained soft-mode dynamics remains local, and loop corrections from hard modes to superhorizon correlators of the adiabatic curvature perturbation are perturbatively suppressed. This provides a model-independent diagnosis of when enhanced corrections due to hard modes can invalidate the gradient expansion. We further show that the same locality condition implies a generalized soft theorem, from which the standard consistency relations follow under additional assumptions. This formulation clarifies the origin of possible deviations from the standard consistency relations in multi-field systems or in a non-attractor background. We also show that the locality condition guarantees the absence of infrared divergences for the correlators of operators invariant under a large gauge transformation. Thus, locality of the hard-mode state provides a unified criterion for the effective description of inflationary soft modes, generalized soft theorems, the suppression of hard-mode loop corrections, and the infrared regularity of observable correlators.

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 formulates a locality condition on the quantum state of hard modes in inflationary cosmology: the hard-mode state in each local patch depends on soft modes only through the local soft-mode values in that patch. When satisfied, this condition implies that coarse-grained soft-mode dynamics remains local, hard-mode loop corrections to superhorizon correlators of the adiabatic curvature perturbation are perturbatively suppressed, a generalized soft theorem holds (from which standard consistency relations follow under further assumptions), and correlators of operators invariant under large gauge transformations are free of infrared divergences. The locality condition is presented as a model-independent diagnostic for the validity of the gradient expansion and separate-universe approach, with implications for multi-field and non-attractor backgrounds.

Significance. If the locality condition can be consistently defined and preserved under inflationary dynamics, the work supplies a unified criterion linking the effective description of soft modes, suppression of hard-mode corrections, generalized soft theorems, and IR regularity. This could clarify the origin of deviations from standard consistency relations and provide a diagnostic for when enhanced hard-mode effects invalidate the gradient expansion. The approach is grounded in the separate-universe and gradient-expansion frameworks standard in the field.

major comments (2)
  1. [Abstract and introduction] The central claim requires that the locality condition be preserved under the unitary time evolution generated by the inflationary Hamiltonian (or under decoherence). The abstract states implications hold 'when this condition is satisfied' but does not appear to contain an explicit derivation or check that the full dynamics maintains the locality property rather than inducing non-local dependence across patches. This is load-bearing for all listed consequences.
  2. [Section on generalized soft theorems] § on generalized soft theorem: the derivation that the locality condition implies the generalized soft theorem (and that standard consistency relations follow under additional assumptions) needs explicit verification against a concrete multi-field or non-attractor example where deviations are known to occur, to confirm the condition is the precise origin of such deviations.
minor comments (2)
  1. [Formulation of locality condition] Clarify the precise mathematical statement of the locality condition (e.g., whether it is formulated in terms of the wavefunctional or density matrix) and its relation to the coarse-graining procedure.
  2. [Introduction] Add a brief discussion of how the condition relates to existing literature on separate-universe approaches and soft theorems (e.g., references to Maldacena, Creminelli et al.).

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive comments. We address the major comments point by point below, indicating the revisions we plan to make.

read point-by-point responses

  1. Referee: [Abstract and introduction] The central claim requires that the locality condition be preserved under the unitary time evolution generated by the inflationary Hamiltonian (or under decoherence). The abstract states implications hold 'when this condition is satisfied' but does not appear to contain an explicit derivation or check that the full dynamics maintains the locality property rather than inducing non-local dependence across patches. This is load-bearing for all listed consequences.

    Authors: We agree that the preservation of the locality condition under the dynamics is a key point. The manuscript defines the condition on the state and derives the consequences assuming it holds at the relevant time. We do not claim that the condition is automatically preserved by the full unitary evolution; rather, it serves as a criterion for the validity of the effective description. In the revised version, we will expand the discussion in the introduction and add a new paragraph explaining how the condition can be preserved under evolution in the inflationary context, particularly when hard modes decouple and decoherence occurs locally. This addresses the load-bearing aspect by clarifying the regime of applicability. revision: yes

  2. Referee: [Section on generalized soft theorems] § on generalized soft theorem: the derivation that the locality condition implies the generalized soft theorem (and that standard consistency relations follow under additional assumptions) needs explicit verification against a concrete multi-field or non-attractor example where deviations are known to occur, to confirm the condition is the precise origin of such deviations.

    Authors: The derivation of the generalized soft theorem is presented as a direct consequence of the locality condition in the dedicated section, without relying on specific model details. It shows how the condition leads to the soft theorem, with standard relations emerging under further assumptions such as attractor behavior. While we do not include a full numerical verification in a specific multi-field model in the current manuscript, the general argument identifies the breakdown of locality as the source of deviations, aligning with known results in the literature for such backgrounds. To strengthen this, we will add in the revision a short discussion referencing a concrete example from the literature (e.g., a multi-field model with known consistency relation violations) and explain how locality is violated there. This provides the requested verification without requiring new computations. revision: partial

Circularity Check

0 steps flagged

No significant circularity: locality condition posited independently with self-contained derivations

full rationale

The paper introduces the locality condition on the quantum state as an explicit premise ('We formulate a locality condition on the quantum state, requiring that the hard-mode state in each local universe depend on the soft modes only through the local soft-mode values in the same patch'). From this assumption it derives the listed consequences for coarse-grained dynamics, loop suppression, generalized soft theorems, and IR regularity. No quoted step reduces any prediction or result to the input by construction, renames a known pattern, or loads the central claim on a self-citation chain whose verification is internal to the present work. The derivation therefore remains logically independent of its starting assumption and does not exhibit any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Based on the abstract alone, the central claims rest on standard domain assumptions of inflationary effective field theory and the separate-universe picture; no explicit free parameters or new invented entities are mentioned.

axioms (2)
  • domain assumption The gradient expansion and separate-universe approach provide a valid effective description of inflationary soft modes after coarse-graining.
    Invoked at the opening of the abstract as the starting point for the effective description.
  • domain assumption Hard-mode states can be defined locally in patches whose size is set by the soft-mode wavelength.
    Implicit in the formulation of the locality condition on the quantum state.

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