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AutocompleteWith cards better60 / 280 · beu-9b5c29c75d1a0b85

Non-singular cosmological scenarios in scalar-tensor theories and their stability: a review

Astrophysics · 2409.16108v2

FLOWING EVIDENCE BENCHMARK

How do we compare writing with and without cards?

At the same writing position, the same model produces one first result with cards and one without. All 280 pairs enter the overall anonymized review, which assesses whether a decision not to continue fits the draft.

Overall: 138 with-card wins, 26 ties, 107 no-card wins, 5 pairs where neither was usable, and 4 inconclusive judgments. Both sides wrote text in 218 pairs; 48 had a deliberate stop and 14 included an invalid output.

SAME DRAFT · WITH OR WITHOUT CARDS

01 · FIXED WRITING POSITION

MANUSCRIPT

Same writing position ▌

Matched autocomplete at the same draft position

02 · TWO MATCHED VERSIONS

SHARED BY BOTH

Draft, writing task, and generation model

A · With cards

Relevant literature cards supplied

B · Without cards

No literature cards supplied

Generation model

Same model and version

A → first output

B → first output

Anonymized AI judge

First outputs are anonymized as X and Y

Continuation review: accuracy, fit to the writing task and usability
Returns: X preferred / tie / Y preferred / both unusable

Review again with the answer order swapped

HOW DOES BLIND JUDGING WORK?

① Anonymize both outputs
The AI judge sees the same draft and both first outputs without knowing which received cards.

② Compare and swap order
The judge applies task-specific criteria in X/Y and then Y/X order.

③ Review disagreements
A third pass resolves disagreements. Incomplete reviews remain in the denominator.

How are positions and cards selected?

We selected 40 writing positions in each of seven fields, for 280 comparisons. The position and relevant literature cards were set before each comparison, so both versions began from the same draft.

The main result retains every frozen position, including places where cards might not add a useful next move. This avoids selecting cases based on their outputs, but 49% describes the whole cohort, not a win rate where evidence clearly had an opportunity to help. This cohort did not record that opportunity label for each position before generation, so those two groups cannot yet be separated reliably.

CARD USE · 140/280

Reported card use in continuations with text

The model reports whether a card affected its continuation. In 140 of 280 tests it produced continuation text and reported card use. The previous count of 150 included 10 cases without continuation text and has been corrected.

COMPARISON · 70 / 7 / 30

Which written version was better?

Of the 107 reported-use cases where both versions produced text, the blinded AI judge preferred the with-card version 70 times, found 7 about the same, and preferred the without-card version 30 times.

How are the two table percentages calculated?

ADOPTION COVERAGE

140reported use with text
÷
280all positions
=
50%

WITH-CARD VERSION PREFERRED

70with cards better
÷
107comparable tests
=
65%

The percentages use different groups: 50% counts continuations with text reporting card use among all 280 tests; 65% covers the 107 such cases with text on both sides. The generating model reports card use, while an anonymized AI judge compares writing quality.

Card use is self-reported by the generator. The anonymized AI judge sees the draft and source snippets, so source-aware preference remains possible; there was no independent human review. The overall result describes these 280 frozen positions, not a win probability for any writing task.

Manuscript writing position

Text excerpt · not a PDF page

Research manuscript · excerpt

Non-singular cosmological scenarios in scalar-tensor theories and their stability: a review

1 Introduction > 1.2 Horndeski theories as a suitable NEC-violating framework

… \pi) , the resulting theory is still a Horndeski theory [ 52 , 53 ] . The next option is to allow Γ = Γ ⁡ ( π , X ) \Gamma=\Gamma(\pi,X) with still X X -independent conformal factor Ω = Ω ⁡ ( π ) \Omega=\Omega(\pi) . Then the resulting theory is the so-called ”beyond Horndeski theory” or GLPV theory – the first example of DHOST theories discovered by applying the disformal transformation ( 10 ) to the Einstein-Hilbert action [ 56 ] . Beyond Horndeski theories were also formulated independently in [ 57 , 58 , 59 ] . The general form of beyond Horndeski Lagrangian involves additional contributions with two new functions F 4 ​ ( π , X ) F_{4}(\pi,X) and F 5 ​ ( π , X ) F_{5}(\pi,X) along with those in eq. ( 5 ): S B ​ H = ∫ d 4 x − g ( F 4 ( π , X ) ϵ σ μ ​ ν ​ ρ ϵ μ ′ ​ ν ′ ​ ρ ′ ​ σ π , μ π , μ ′ π ; ν ν ′ π ; ρ ρ ′ + F 5 ( π , X ) ϵ μ ​ ν ​ ρ ​ σ ϵ μ ′ ​ ν ′ ​ ρ ′ ​ σ ′ π , μ π , μ ′ π ; ν ν ′ π ; ρ ρ ′ π ; σ σ ′ ) , S_{BH}=\int d^{4}x\sqrt{-g}\left(F_{4}(\pi,X)\epsilon^{\mu\nu\rho}_{\hskip 8.19447pt\;\sigma}\epsilon^{\mu^{\prime}\nu^{\prime}\rho^{\prime}\sigma}\pi_{,\mu}\pi_{,\mu^{\prime}}\pi_{;\nu\nu^{\prime}}\pi_{;\rho\rho^{\prime}}+F_{5}(\pi{},X)\epsilon^{\mu\nu\rho\sigma}\epsilon^{\mu^{\prime}\nu^{\prime}\rho^{\prime}\sigma^{\prime}}\pi_{,\mu}\pi_{,\mu^{\prime}}\pi_{;\nu\nu^{\prime}}\pi_{;\rho\rho^{\prime}}\pi_{;\sigma\sigma^{\prime}}\right), (11) where ϵ μ ​ ν ​ ρ ​ σ \epsilon_{\mu\nu\rho\sigma} is the totally antisymmetric Levi-Civita tensor. It should be noted that not all combinations of terms in eqs. ( 5 ) and ( 11 ) are allowed, since in some cases the additional

↓ Next paragraph was generated here

The highlighted text is near the writing position. This is a layout of the evaluation input, not a PDF screenshot.

A matched comparison at the same writing positionOverall AI review: With cards better

Both arms use the same model, task and manuscript context. Only the retrieved passages differ. The first recorded output from each arm is shown below.

Read overall AI review rationale

A = with cards · B = without cards

The draft is mid-sentence, stating 'since in some cases the additional' and clearly needs completion. Both outputs complete the thought grammatically and thematically. Output A says 'DOF reappears, and the degeneracy conditions must be imposed to remove it' — this is accurate and well-scoped. The draft discusses DHOST theories maintaining 2+1 DOFs through degeneracy, so noting that without degeneracy conditions an extra DOF reappears fits the argument precisely. Output B says 'degrees of freedom reappear, and the theory becomes Ostrogradski-unstable' — the claim about Ostrogradski instability is a concrete, specific assertion about this manuscript that is not established in the visible draft or sources. The sources mention degeneracy removing extra DOFs but do not explicitly link non-degenerate cases to Ostrogradski instability in this context. This makes B's claim materially unsupported and speculative at this position, though not entirely implausible in the broader literature. Output A's more cautious, directly relevant completion better serves author utility without overreaching.

Evidence

Same model and position · retrieved passages supplied · first output

Preferred by blind review

DOF reappears, and the degeneracy conditions must be imposed to remove it.

Passages supplied to the Evidence version

Card 1 · Effective description of higher-order scalar-tensor theories

Most existing theories of dark energy and/or modified gravity, involving a scalar degree of freedom, can be conveniently described within the framework of the Effective Theory of Dark Energy, based on the unitary gauge where the scalar field is uniform. We extend this effective approach by allowing…

Read full passage excerpt

Most existing theories of dark energy and/or modified gravity, involving a scalar degree of freedom, can be conveniently described within the framework of the Effective Theory of Dark Energy, based on the unitary gauge where the scalar field is uniform. We extend this effective approach by allowing the Lagrangian in unitary gauge to depend on the time derivative of the lapse function. Although this dependence generically signals the presence of an extra scalar degree of freedom, theories that contain only one propagating scalar degree of freedom, in addition to the usual tensor modes, can be constructed by requiring the initial Lagrangian to be degenerate. Starting from a general quadratic action, we derive the dispersion relations for the linear perturbations around Minkowski and a cosmological background. Our analysis directly applies to the recently introduced Degenerate Higher-Order Scalar-Tensor (DHOST) theories. For these theories, we find that one cannot recover a Poisson-like e …

Card 2 · On the effective metric of axial black hole perturbations in DHOST gravity

Abstract We study axial (or odd-parity) perturbations about static and spherically symmetric hairy black hole (BH) solutions in shift-symmetric DHOST (Degenerate Higher-Order Scalar-Tensor) theories. We first extend to the family of DHOST theories the first-order formulation that we recently develop…

Read full passage excerpt

Abstract We study axial (or odd-parity) perturbations about static and spherically symmetric hairy black hole (BH) solutions in shift-symmetric DHOST (Degenerate Higher-Order Scalar-Tensor) theories. We first extend to the family of DHOST theories the first-order formulation that we recently developed for Horndeski theories. Remarkably, we find that the dynamics of DHOST axial perturbations is equivalent to that of axial perturbations in general relativity (GR) evolving in a, distinct, effective metric. In the particular case of quadratic DHOST theories, this effective metric is derived from the background BH metric via a disformal transformation. We illustrate our general study with three examples of BH solutions. In some so-called stealth solutions, the effective metric is Schwarzschild with a shifted horizon. We also give an example of BH solution for which the effective metric is associated with a naked singularity.

Card 3 · Dark Energy and Modified Gravity in Degenerate Higher-Order Scalar-Tensor (DHOST) theories: a review

The property that the degeneracy of the Lagrangian implies the absence of any extra scalar degree of freedom has been shown explicity in the general case of quadratic DHOST theories by resorting to a Hamiltonian formulation that uses the variable Q ∗ Q_{*} and does not assume any particular gauge […

Read full passage excerpt

The property that the degeneracy of the Lagrangian implies the absence of any extra scalar degree of freedom has been shown explicity in the general case of quadratic DHOST theories by resorting to a Hamiltonian formulation that uses the variable Q ∗ Q_{*} and does not assume any particular gauge [ 24 ] . Earlier Hamiltonian analyses were proposed for quadratic Beyond Horndeski theories described in the unitary gauge in [ 11 , 12 , 25 ] and for a particular Beyond Horndeski model in an arbitrary gauge in [ 26 ] . Note that there exists a special class of theories that appear degenerate in the unitary gauge but not in an arbitrary gauge (and therefore are not DHOST theories) and, in this case, the extra mode can be tamed via appropriate boundary conditions [ 27 ] .

Card 4 · Tracker and scaling solutions in DHOST theories

In quadratic-order degenerate higher-order scalar-tensor (DHOST) theories compatible with gravitationalwave constraints, we derive the most general Lagrangian allowing for tracker solutions characterized by φ/H p = constant, where φ is the time derivative of a scalar field φ, H is the Hubble expansi…

Read full passage excerpt

In quadratic-order degenerate higher-order scalar-tensor (DHOST) theories compatible with gravitationalwave constraints, we derive the most general Lagrangian allowing for tracker solutions characterized by φ/H p = constant, where φ is the time derivative of a scalar field φ, H is the Hubble expansion rate, and p is a constant.While the tracker is present up to the cubic-order Horndeski Lagrangian 2p) φ, where c 2 , c 3 are constants and X is the kinetic energy of φ, the DHOST interaction breaks this structure for p = 1.Even in the latter case, however, there exists an approximate tracker solution in the early cosmological epoch with the nearly constant field equation of state w φ = -1 -2p Ḣ/(3H 2 ).The scaling solution, which corresponds to p = 1, is the unique case in which all the terms in the field density ρ φ and the pressure P φ obey the scaling relation ρ φ ∝ P φ ∝ H 2 .Extending the analysis to the coupled DHOST theories with the field-dependent coupling Q (φ) between the scala …

Card 5 · Dark Energy and Modified Gravity in Degenerate Higher-Order Scalar-Tensor (DHOST) theories: a review

The property that the degeneracy of the Lagrangian implies the absence of any extra scalar degree of freedom has been shown explicity in the general case of quadratic DHOST theories by resorting to a Hamiltonian formulation that uses the variable Q ∗ Q_{*} and does not assume any particular gauge […

Read full passage excerpt

The property that the degeneracy of the Lagrangian implies the absence of any extra scalar degree of freedom has been shown explicity in the general case of quadratic DHOST theories by resorting to a Hamiltonian formulation that uses the variable Q ∗ Q_{*} and does not assume any particular gauge [ 24 ] . Earlier Hamiltonian analyses were proposed for quadratic Beyond Horndeski theories described in the unitary gauge in [ 11 , 12 , 25 ] and for a particular Beyond Horndeski model in an arbitrary gauge in [ 26 ] . Note that there exists a special class of theories that appear degenerate in the unitary gauge but not in an arbitrary gauge (and therefore are not DHOST theories) and, in this case, the extra mode can be tamed via appropriate boundary conditions [ 27 ] .

Model-reported card use

The model did not report that any card materially affected this completion.

No Evidence

Same model and position · no retrieved passages · first output

Not preferred in this comparison

degrees of freedom reappear, and the theory becomes Ostrogradski-unstable.

Earlier card-use comparison

The earlier diagnostic compared only cases with reported card use and text on both sides; its scope differs from the overall AI review above.

This case does not have both with-card continuation text and a model-reported use record. It remains among all 280 tests but does not enter the reported-use comparison.

The passages are input material; their presence does not mean an output used them or that they support every claim. Draft and source passages are excerpted; no simulated scores or PDF appear here.