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arxiv: 2606.20730 · v1 · pith:JCNWSXG7new · submitted 2026-06-17 · 🌀 gr-qc · hep-th

Scalar-scalar-tensor interaction in DHOST theories

S. Mironov , V. Volkova This is my paper

Pith reviewed 2026-06-26 20:28 UTC · model grok-4.3

classification 🌀 gr-qc hep-th
keywords DHOST theoriescubic actionscalar-scalar-tensor interactionscosmological perturbationsgravitational wave decaydark energyunitary gauge
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0 comments X

The pith

Quadratic DHOST theories have a general cubic action for scalar-scalar-tensor perturbations around cosmological backgrounds.

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

The paper derives the general cubic action for perturbations about a cosmological background in the quadratic subclass of DHOST theories. It focuses on the scalar-scalar-tensor interactions using a fully covariant formulation and unitary gauge. This mixed sector is the key for estimating how gravitational waves decay into two scalar excitations. A sympathetic reader would care because these interactions determine the viability of DHOST models as descriptions of late-time dark energy.

Core claim

We derive the general cubic action for perturbations about a cosmological background in the quadratic subclass of degenerate higher-order scalar-tensor (DHOST) theories, focusing on scalar-scalar-tensor interactions. We adopt a fully covariant formulation and implement unitary gauge at the level of perturbations. This mixed sector provides the key ingredient for estimating the decay rate of a gravitational wave into two scalar excitations in the quadratic DHOST models of dark energy in the late-time Universe.

What carries the argument

The cubic scalar-scalar-tensor interaction terms in the perturbation action around a cosmological background, obtained via covariant formulation with unitary gauge.

If this is right

  • The derived cubic action supplies the interaction vertices needed to compute the decay rate of gravitational waves into scalar excitations.
  • The results apply to quadratic DHOST models intended as descriptions of dark energy in the late-time Universe.
  • Unitary gauge at the perturbation level isolates the scalar-scalar-tensor mixing without altering the degeneracy conditions of the original theory.

Where Pith is reading between the lines

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

  • The explicit form of the cubic terms could be inserted into Boltzmann codes or N-body simulations to place bounds on DHOST parameters from gravitational-wave observations.
  • The same covariant-plus-unitary-gauge procedure might be applied to quartic or higher interactions to check consistency across the full effective action.

Load-bearing premise

The quadratic subclass of DHOST theories remains a valid effective description for late-time dark energy without introducing additional instabilities or degrees of freedom when the cubic scalar-scalar-tensor sector is included.

What would settle it

An explicit computation from the derived cubic action that produces ghost modes or extra propagating degrees of freedom on a late-time cosmological background would show the sector cannot be added while preserving the theory's viability.

read the original abstract

We derive the general cubic action for perturbations about a cosmological background in the quadratic subclass of degenerate higher-order scalar-tensor (DHOST) theories, focusing on scalar-scalar-tensor interactions. We adopt a fully covariant formulation and implement unitary gauge at the level of perturbations. This mixed sector provides the key ingredient for estimating the decay rate of a gravitational wave into two scalar excitations in the quadratic DHOST models of dark energy in the late-time 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

0 major / 2 minor

Summary. The manuscript derives the general cubic action for cosmological perturbations in the quadratic subclass of DHOST theories, restricting attention to the scalar-scalar-tensor sector. The derivation is performed in a fully covariant manner with unitary gauge imposed at the perturbative level; the resulting action is presented as the essential ingredient for computing the decay rate of gravitational waves into scalar modes in late-time DHOST dark-energy models.

Significance. If the derivation is correct, the work supplies a concrete, general expression for the cubic scalar-scalar-tensor vertices that can be used to evaluate interaction rates and stability properties in quadratic DHOST cosmologies. This is a technical but useful step for connecting the degeneracy conditions of DHOST theories to observable gravitational-wave phenomenology.

minor comments (2)
  1. The abstract states that the cubic action is derived but does not display the final expression or the degeneracy conditions retained at cubic order; including the explicit Lagrangian (perhaps in an appendix) would improve readability without altering the central claim.
  2. Notation for the background quantities (e.g., the Hubble parameter and scalar-field velocity) should be defined once at first appearance rather than re-introduced in each section.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript and for recommending acceptance. The work is presented as a technical contribution supplying the cubic scalar-scalar-tensor vertices for quadratic DHOST cosmologies.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper states it derives the cubic action directly from the quadratic DHOST Lagrangian via covariant formulation and unitary gauge at the perturbation level. No equations or steps are shown to reduce by construction to fitted inputs, self-definitions, or load-bearing self-citations; the derivation is presented as an independent expansion of the known action. The reader's assessment of score 2.0 aligns with this being a standard non-circular derivation from established theory.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Based solely on the abstract; the central claim rests on the standard degeneracy conditions of DHOST theories and the choice of quadratic subclass.

axioms (2)
  • domain assumption The theory belongs to the quadratic subclass of DHOST theories
    Explicitly stated as the setting for the derivation and for dark energy modeling
  • domain assumption Unitary gauge can be implemented at the level of perturbations without loss of generality
    Method stated in the abstract

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discussion (0)

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Reference graph

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