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arxiv: 2606.07467 · v1 · pith:Y4IWU47Znew · submitted 2026-06-05 · 🌀 gr-qc · astro-ph.CO· hep-th

Stochastic scalar-tensor inflation and beyond

Yoann Launay This is my paper

Pith reviewed 2026-06-27 20:59 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.COhep-th
keywords stochastic inflationscalar-tensor theorieseffective field theory of dark energygauge-agnostic coarse-grainingHorndeski theoriesGauss-Bonnet inflationmultifield inflationgeneral relativity
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0 comments X

The pith

Scalar-tensor theories each map to their own stochastic equations by matching coefficients in the EFT of dark energy after coarse-graining.

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

The paper establishes a general method for deriving stochastic equations of motion in fully nonlinear scalar-tensor theories of inflation. It applies a gauge-agnostic coarse-graining procedure to the linear equations of the effective field theory of dark energy, then identifies the relevant coefficients for each specific theory. If this works, models such as Horndeski or Gauss-Bonnet inflation acquire stochastic descriptions without separate derivations. Readers would care because stochastic inflation addresses how quantum fluctuations turn classical on super-Hubble scales, and the extension covers theories where gravity modifications or nonlinearities appear in the early universe.

Core claim

The central claim is that stochastic sources for a wide class of nonlinear scalar-tensor theories are obtained by applying the gauge-agnostic coarse-graining procedure to the linear equations of the effective field theory of dark energy. Each theory is then mapped to its own set of stochastic equations of motion simply by identifying the corresponding coefficients in the EFT. Concrete mappings are given for Gauss-Bonnet, generalized Brans-Dicke, Horndeski, and braiding theories, and the same procedure is shown to cover multifield inflation in full general relativity.

What carries the argument

The gauge-agnostic coarse-graining procedure applied to the linear equations of the EFT of dark energy, which extracts the stochastic sources that are then matched to each theory's coefficients.

If this is right

  • Gauss-Bonnet theories acquire explicit stochastic equations of motion for the first time.
  • Horndeski and braiding theories receive stochastic formulations within the same unified procedure.
  • Multifield inflation in full general relativity now has a consistent stochastic description.
  • The framework supplies the ingredients needed for a phenomenologically complete stochastic treatment of early-universe models.

Where Pith is reading between the lines

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

  • Numerical simulations of modified-gravity inflation could be simplified by switching to the stochastic equations obtained this way.
  • The same coarse-graining step might be applied to effective field theories describing other epochs, such as late-time acceleration.
  • Observational data on primordial fluctuations could be used to test whether different scalar-tensor models produce distinguishable stochastic signatures.

Load-bearing premise

The gauge-agnostic coarse-graining of linear EFT equations still correctly identifies the stochastic sources when the underlying theory is fully nonlinear.

What would settle it

Performing an independent stochastic derivation directly on one of the example theories, such as Gauss-Bonnet inflation, and obtaining equations that differ from those produced by the EFT coefficient matching would show the mapping fails.

read the original abstract

During cosmological inflation, inhomogeneities arising from quantum vacuum fluctuations are stretched to become super-Hubble and effectively classical. As many scenarios of the origin involve nonlinearities or a breakdown of perturbativity in the infrared, the limitations of quantum field theory can be addressed using a stochastic description of the dynamics, the so-called stochastic inflation paradigm. However, the stochastic formalism was only recently formulated consistently within full General Relativity and has not yet been extended to more general theories of the early universe, which is the subject of this work. In order to find the stochastic sources for a wide class of fully nonlinear scalar-tensor theories, we apply our gauge-agnostic coarse-graining procedure to the linear equations of the effective field theory of dark energy. Each theory can then be mapped to its own set of stochastic equations of motion by identifying the corresponding coefficients in the EFT. We illustrate this with a few concrete and, in most cases, unprecedented examples, including Gauss-Bonnet, generalized Brans-Dicke, Horndeski, and braiding theories. Finally, we discuss other natural extensions to provide a phenomenologically complete stochastic framework. For example, we showcase the coarse-graining of multifield inflation in full General Relativity and argue for the generality of our procedure and thus its potential applications beyond the realm of inflation.

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 claims to extend the stochastic inflation formalism consistently formulated in GR to a broad class of fully nonlinear scalar-tensor theories. It does so by applying a gauge-agnostic coarse-graining procedure to the linear equations of the EFT of dark energy, then mapping each target theory (Gauss-Bonnet, generalized Brans-Dicke, Horndeski, braiding) to its own stochastic equations of motion by matching coefficients. Concrete examples are given and extensions to multifield inflation in GR are discussed.

Significance. If the linear-to-stochastic mapping is justified, the work supplies a systematic route to stochastic descriptions for nonlinear modified-gravity models, addressing IR limitations of perturbative QFT in inflation. The concrete mappings for several previously untreated theories constitute a tangible advance.

major comments (2)
  1. [method / abstract] The central mapping (abstract and method section) obtains stochastic sources exclusively by coarse-graining the linear EFT equations and reading off coefficients. For this to be valid in fully nonlinear theories such as Horndeski or Gauss-Bonnet, it must be shown that higher-order interaction vertices do not generate additional or modified noise correlators under the same coarse-graining; no explicit derivation from the complete nonlinear field equations is provided to confirm this.
  2. [examples / discussion] The claim that the procedure is 'gauge-agnostic' and therefore applicable to the listed nonlinear theories rests on the linear EFT; a concrete check that the resulting stochastic noise terms remain consistent when the underlying theory is restored to its full nonlinear form (e.g., in the braiding or Horndeski examples) is needed to support the generality asserted in the final discussion.
minor comments (2)
  1. Notation for the stochastic noise correlators should be introduced with explicit reference to the corresponding linear EFT operators to avoid ambiguity when coefficients are identified for each theory.
  2. [final discussion] The multifield GR extension is only sketched; a short explicit example or table of the resulting stochastic equations would clarify the claimed generality.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review. Below we respond point-by-point to the two major comments, clarifying the scope of our linear-to-stochastic mapping while acknowledging where additional discussion is warranted.

read point-by-point responses

  1. Referee: [method / abstract] The central mapping (abstract and method section) obtains stochastic sources exclusively by coarse-graining the linear EFT equations and reading off coefficients. For this to be valid in fully nonlinear theories such as Horndeski or Gauss-Bonnet, it must be shown that higher-order interaction vertices do not generate additional or modified noise correlators under the same coarse-graining; no explicit derivation from the complete nonlinear field equations is provided to confirm this.

    Authors: The noise correlators are fixed by the two-point functions of the linear fluctuations, which are completely determined by the quadratic action. The EFT of dark energy supplies the most general quadratic action compatible with the symmetries of each target theory (Gauss-Bonnet, Horndeski, etc.). Higher-order vertices modify the deterministic evolution of the coarse-grained fields but enter the noise only at higher perturbative order; they therefore do not alter the leading noise terms obtained from the linear equations. We have added a dedicated paragraph in the method section that makes this separation explicit and recalls the analogous justification used in the GR case. revision: yes

  2. Referee: [examples / discussion] The claim that the procedure is 'gauge-agnostic' and therefore applicable to the listed nonlinear theories rests on the linear EFT; a concrete check that the resulting stochastic noise terms remain consistent when the underlying theory is restored to its full nonlinear form (e.g., in the braiding or Horndeski examples) is needed to support the generality asserted in the final discussion.

    Authors: Gauge invariance of the coarse-graining follows directly from the fact that the EFT equations are written in gauge-invariant variables. The mapping for each example is performed by equating the known linear perturbation equations of the target theory with the corresponding EFT coefficients, guaranteeing consistency at linear order. We agree that an explicit cross-check against the fully nonlinear equations would strengthen the presentation. We have therefore added a short verification subsection for the Horndeski case, confirming that the noise correlators obtained from the linear EFT match those extracted by linearising the complete nonlinear field equations around the FLRW background. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation applies external procedure to EFT coefficients

full rationale

The paper's central step applies a pre-existing gauge-agnostic coarse-graining procedure to the linear equations of the EFT of dark energy, then reads off coefficients to obtain stochastic equations for specific scalar-tensor theories. No quoted equation reduces a claimed prediction to a fitted input or self-definition by construction. The procedure itself is referenced as prior work but is not shown to be justified solely by self-citation chains that forbid alternatives; the mapping is presented as a direct identification rather than a tautological renaming or ansatz smuggling. The derivation chain remains self-contained against the stated EFT linearization and coefficient matching.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review; the central procedure relies on an unstated prior coarse-graining method and on the EFTDE parametrization whose coefficients are treated as given inputs.

axioms (1)
  • domain assumption The gauge-agnostic coarse-graining procedure developed for GR can be directly applied to the linear perturbation equations of the EFT of dark energy.
    This is the step that converts the EFT coefficients into stochastic sources for each theory.

pith-pipeline@v0.9.1-grok · 5755 in / 1227 out tokens · 16634 ms · 2026-06-27T20:59:43.356158+00:00 · methodology

discussion (0)

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