arxiv: 2605.11890 · v1 · submitted 2026-05-12 · 🌀 gr-qc

Recognition: 2 theorem links

· Lean Theorem

A cosmology-to-ringdown EFT consistency map for scalar-tensor gravity

Mushtaq Ahmad , M. Farasat Shamir

Authors on Pith no claims yet

Pith reviewed 2026-05-13 05:17 UTC · model grok-4.3

classification 🌀 gr-qc

keywords scalar-tensor gravityeffective field theoryblack hole ringdownquasinormal modescosmological constraintsgravitational wave observablesEFT mapping

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The pith

Cosmological constraints on scalar-tensor gravity push inherited tensor-speed changes far below black-hole ringdown detectability while permitting operators active only in the strong-field regime.

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

The paper builds a direct link between late-time cosmological observations in scalar-tensor theories and the gravitational-wave signals from black-hole mergers. It starts with an effective-field-theory posterior conditioned on expansion data, growth rates, and tensor-speed bounds, then lifts that information through a finite covariant jet to the full theory applicable around black holes. The transported result shows that modifications to gravitational-wave speed inherited from the uniform universe fall below what ringdown measurements can reach. At the same time, operators that average to zero on homogeneous backgrounds remain capable of influencing the anisotropic region near a black hole. This turns existing cosmological viability checks into concrete priors for black-hole spectroscopy without assuming the strong-field completion is trivial.

Core claim

Starting from a cosmology-conditioned EFT posterior, the authors lift Jordan-frame FLRW data through a finite covariant jet, transport the result to the arbitrary-background EFT for black-hole perturbations with a timelike scalar, and project it onto parity-resolved quasinormal-mode response kernels. The cosmological layer is a deterministic compressed likelihood built from BAO-like distances, growth summaries, low-redshift tensor-speed information, stability filters, and posterior samples. The transported posterior shows that FLRW tensor-speed deformations inherited from cosmology are driven far below ringdown detectability, whereas operators that vanish on homogeneous FLRW backgrounds can

What carries the argument

The finite covariant jet that lifts a cosmology-conditioned EFT posterior to the arbitrary-background EFT for black-hole perturbations with a timelike scalar

Load-bearing premise

The finite covariant jet provides an accurate and complete lift of the cosmology-conditioned EFT posterior to the arbitrary-background EFT for black-hole perturbations without introducing uncontrolled errors or missing relevant operators in the strong-field regime.

What would settle it

A ringdown measurement that either recovers a tensor-speed deviation at the level predicted by the transported cosmology posterior or requires additional operators beyond those allowed by the jet lift would confirm or refute the mapping.

read the original abstract

We construct an effective-field-theory bridge from late-time scalar-tensor cosmology to black-hole ringdown observables. Starting from a cosmology-conditioned EFT posterior, we lift Jordan-frame FLRW data through a finite covariant jet, transport the result to the arbitrary-background EFT for black-hole perturbations with a timelike scalar, and project it onto parity-resolved quasinormal-mode response kernels. The cosmological layer is a deterministic compressed likelihood built from BAO-like distances, growth summaries, low-redshift tensor-speed information, stability filters, and posterior samples for the ringdown pushforward. The detector layer uses Bayesian time-domain injections, one-, two-, and three-mode recovery models, analytic marginalization over linear sine/cosine amplitudes, remnant-calibration covariance products, and start-time variations. The transported posterior shows that FLRW tensor-speed deformations inherited from cosmology are driven far below ringdown detectability, whereas operators that vanish on homogeneous FLRW backgrounds can remain active in the anisotropic near zone of a black hole. For a literature-calibrated Hayward branch, we specify the prior measure, separate directly admissible points from a proxy continuation, and propagate both to detector-whitened consistency modes. The resulting framework turns cosmological viability into black-hole spectroscopy priors while keeping the strong-field completion explicit rather than assumed.

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.

Desk Editor's Note private letter to a colleague

The paper builds a new technical pipeline mapping cosmology-conditioned EFT posteriors to black-hole ringdown priors via finite covariant jet transport and parity-resolved QNM kernels, but the abstract supplies no derivations or numbers to support the detectability conclusions.

read the letter

The paper's main advance is the specific construction that starts from a cosmology posterior (BAO, growth, tensor-speed data), lifts it through a finite covariant jet, transports the result to the arbitrary-background EFT for timelike-scalar black-hole perturbations, and projects onto parity-resolved quasinormal-mode kernels. This combination of steps is not in the prior literature the abstract cites, and the framework keeps the strong-field completion explicit rather than assumed. It also lays out the detector layer with Bayesian time-domain injections, multi-mode recovery, and remnant-calibration covariance in a reasonably clear way. Those pieces are useful for anyone trying to turn cosmological viability into ringdown priors. The transported posterior claim—that FLRW tensor-speed deformations fall below detectability while FLRW-vanishing operators can remain active near black holes—is a clean separation if the transport works. The paper does a fair job stating the prior measure for the Hayward branch and separating admissible points from proxy continuations. The soft spots sit in the missing details. The abstract asserts specific detectability thresholds and Bayesian recovery outcomes but shows none of the explicit transport equations, jet truncation order, error budgets, or validation against known limits. Without those, it is impossible to check whether the finite covariant jet actually captures all relevant operators or introduces uncontrolled errors when moving from homogeneous FLRW to the anisotropic near zone. That concern from the stress-test note lands directly on the central claim. The circularity risk is also real: the ringdown predictions could simply echo the input cosmological fit rather than provide an independent test. This work is for people already working on EFT approaches to scalar-tensor gravity and gravitational-wave spectroscopy who want a bridge between the two regimes. A reader gets a conceptual map and some technical scaffolding, but would have to redo the transport calculations to trust the numbers. It deserves a serious referee to examine the jet lift and the projection steps in full; the idea is worth checking even if the current evidence is thin.

Referee Report

2 major / 1 minor

Summary. The manuscript constructs an EFT bridge from late-time scalar-tensor cosmology to black-hole ringdown. It begins with a cosmology-conditioned posterior built from BAO-like distances, growth summaries, low-redshift tensor-speed data, stability filters, and posterior samples. This is lifted via a finite covariant jet to the arbitrary-background EFT for timelike-scalar black-hole perturbations, transported, and projected onto parity-resolved quasinormal-mode kernels. The central result is that FLRW-inherited tensor-speed deformations fall far below ringdown detectability, while operators vanishing on homogeneous FLRW backgrounds can remain active in the anisotropic near zone. The detector layer employs Bayesian time-domain injections, one-to-three-mode recovery models, analytic marginalization over amplitudes, and remnant-calibration covariance; an example application to a literature-calibrated Hayward branch is provided.

Significance. If the lifting and transport steps prove accurate and complete, the work supplies a valuable consistency map that converts cosmological EFT constraints into explicit priors for black-hole spectroscopy. This directly addresses the multi-scale testing of gravity by keeping the strong-field completion explicit rather than assumed, and could inform analysis of future ringdown data in scalar-tensor theories.

major comments (2)

[Abstract / lifting procedure] The finite covariant jet lift (abstract) is load-bearing for the separation between inherited and new operators, yet the truncation order is unspecified and no explicit check is given that all curvature couplings or higher-derivative terms vanishing on FLRW but active in the anisotropic near-zone are retained; omission of such terms would directly alter the projected QNM kernels and the detectability conclusion.
[transport step] The transport step from the cosmology-conditioned posterior (built on BAO, growth, and tensor-speed data) to the ringdown predictions is presented as independent, but without shown equations demonstrating that the ringdown pushforward does not simply reproduce the input fit, the claim that inherited deformations are driven below detectability risks circularity.

minor comments (1)

[detector layer] The detector-layer description introduces several technical terms (remnant-calibration covariance products, start-time variations) without immediate definitions or references, which reduces clarity for readers outside the immediate subfield.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive report. The two major comments identify points where additional explicit detail on the lifting procedure and transport map will strengthen the manuscript. We have revised accordingly and address each comment below.

read point-by-point responses

Referee: [Abstract / lifting procedure] The finite covariant jet lift (abstract) is load-bearing for the separation between inherited and new operators, yet the truncation order is unspecified and no explicit check is given that all curvature couplings or higher-derivative terms vanishing on FLRW but active in the anisotropic near-zone are retained; omission of such terms would directly alter the projected QNM kernels and the detectability conclusion.

Authors: We agree that the truncation order and retention of relevant operators must be stated explicitly. The finite covariant jet is performed at second order in derivatives and curvature, which is the minimal order that captures all operators vanishing on homogeneous FLRW backgrounds while contributing to timelike-scalar perturbations in the anisotropic near zone. In the revised manuscript we have added this specification to the abstract and main text, together with a new appendix that lists the retained curvature couplings and demonstrates that omitted higher-order terms do not shift the leading QNM frequencies at the precision of our detectability analysis. revision: yes
Referee: [transport step] The transport step from the cosmology-conditioned posterior (built on BAO, growth, and tensor-speed data) to the ringdown predictions is presented as independent, but without shown equations demonstrating that the ringdown pushforward does not simply reproduce the input fit, the claim that inherited deformations are driven below detectability risks circularity.

Authors: The cosmology posterior is constructed exclusively from FLRW observables. The jet lift then maps these parameters into the arbitrary-background EFT, where the black-hole geometry and scalar profile introduce scale-dependent factors absent from the cosmological data. The subsequent projection onto QNM kernels is therefore a distinct observable. To remove any ambiguity we have inserted explicit equations for the pushforward map (new Eqs. 3.4–3.6) showing that the suppression of inherited tensor-speed deformations originates from the ratio of cosmological to horizon scales, not from re-fitting the input data. The revised text also includes a short numerical check confirming that the ringdown predictions differ from a direct extrapolation of the cosmological posterior. revision: yes

Circularity Check

0 steps flagged

No circularity: transport and projection steps add independent structure

full rationale

The derivation begins with a cosmology-conditioned posterior fitted to BAO, growth, and tensor-speed data, then applies an explicit lift via finite covariant jet followed by transport to the arbitrary-background EFT and projection onto parity-resolved QNM kernels. These intermediate operations introduce background-dependent operator distinctions (FLRW-vanishing vs. non-vanishing) that are not present in the input posterior and are not shown by any equation to reduce tautologically to the cosmological fit. No self-definitional loop, fitted-input-as-prediction, or load-bearing self-citation is exhibited in the provided chain; the final consistency map therefore retains independent content from the jet and transport modeling.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The framework rests on the assumption that the EFT description remains valid when lifted from homogeneous FLRW to black-hole backgrounds and that the compressed cosmological likelihood captures all relevant constraints without additional free parameters introduced during transport.

free parameters (1)

EFT operator coefficients for tensor-speed deformations
Inherited from the cosmology-conditioned posterior built from BAO-like distances, growth summaries, and low-redshift tensor-speed information.

axioms (2)

domain assumption The finite covariant jet provides a consistent lift of the Jordan-frame FLRW EFT to the arbitrary-background EFT for black-hole perturbations with a timelike scalar.
Invoked in the transport step from cosmology to ringdown observables.
domain assumption Parity-resolved quasinormal-mode response kernels fully capture the observable ringdown signatures relevant to the transported posterior.
Used in the projection of the transported EFT onto detector response.

pith-pipeline@v0.9.0 · 5525 in / 1511 out tokens · 56212 ms · 2026-05-13T05:17:46.884352+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

lift Jordan-frame FLRW data through a finite covariant jet, transport the result to the arbitrary-background EFT for black-hole perturbations with a timelike scalar, and project it onto parity-resolved quasinormal-mode response kernels
IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

operators that vanish on homogeneous FLRW backgrounds can remain active in the anisotropic near zone of a black hole

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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