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arxiv: 2311.12104 · v3 · submitted 2023-11-20 · 🌀 gr-qc · hep-th

Cosmological higher-curvature gravities

Javier Moreno , \'Angel J. Murcia This is my paper

Pith reviewed 2026-05-24 05:04 UTC · model grok-4.3

classification 🌀 gr-qc hep-th
keywords higher-curvature gravitycosmological perturbationsFLRW backgroundsmodified gravitysecond-order equationsscalar perturbationshigher-derivative gravity
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The pith

Higher-curvature gravity theories with second-order FLRW equations also produce at most second-order linearized equations for scalar cosmological perturbations.

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

The paper introduces Cosmological Gravities as higher-curvature theories whose FLRW background equations of motion stay second order in derivatives, matching Einstein gravity. It gives explicit constructions of such theories to all curvature orders in D greater than or equal to 3, plus versions that admit single-function generalizations of the Schwarzschild solution in D greater than or equal to 4. The central result states that any Cosmological Gravity in D greater than or equal to 3 yields linearized scalar perturbation equations containing no more than two time derivatives. This holds for generic choices of the higher-curvature terms and is verified explicitly in four-dimensional examples through fifth order in curvature.

Core claim

In any Cosmological Gravity, defined as a higher-curvature gravity whose FLRW configurations satisfy second-order equations of motion, the linearized equations of motion for scalar cosmological perturbations in D greater than or equal to 3 contain no more than two time derivatives. This is shown by explicit calculation in specific four-dimensional examples up to fifth curvature order, and argued to hold generally.

What carries the argument

Cosmological Gravities: higher-curvature theories restricted so that FLRW background equations remain second order in derivatives.

If this is right

  • Explicit constructions of Cosmological Gravities exist for all curvature orders in D greater than or equal to 3.
  • Non-hairy Schwarzschild generalizations with at most second-order equations exist for D greater than or equal to 4.
  • The at-most-two-derivatives property for scalar perturbations holds for generic Cosmological Gravities in D greater than or equal to 3.
  • The property is verified up to fifth order in curvature in four-dimensional examples.

Where Pith is reading between the lines

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

  • The background restriction may automatically control higher time derivatives across a wider class of perturbations.
  • The same construction method could be tested on vector or tensor modes to check for similar behavior.
  • These theories supply a route to building higher-curvature models for cosmology that avoid extra propagating degrees of freedom from higher derivatives.

Load-bearing premise

The higher-curvature terms can be chosen so that the FLRW background equations remain second order in derivatives; the general perturbation result is then claimed to follow for any such choice.

What would settle it

Explicitly computing the linearized scalar perturbation equations in one explicit Cosmological Gravity in D=3 or D=4 and finding a term with three or more time derivatives.

read the original abstract

We examine higher-curvature gravities whose FLRW configurations are specified by equations of motion which are of second order in derivatives, just like in Einstein gravity. We name these theories Cosmological Gravities and initiate a systematic exploration in dimensions $D \geq 3$. First, we derive an instance of Cosmological Gravity to all curvature orders and dimensions $D \geq 3$. Second, we study Cosmological Gravities admitting non-hairy generalizations of the Schwarzschild solution characterized by a single function whose equation of motion is, at most, of second order in derivatives. We present explicit instances of such theories for all curvature orders and dimensions $D \geq 4$. Finally, we investigate the equations of motion for cosmological perturbations in the context of generic Cosmological Gravities. Remarkably, we find that the linearized equations of motion for scalar cosmological perturbations in any Cosmological Gravity in $D\geq 3$ contain no more than two time derivatives. We explicitly corroborate this aspect by presenting the equations for the scalar perturbations in some four-dimensional Cosmological Gravities up to fifth order in the curvature.

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

1 major / 0 minor

Summary. The paper defines 'Cosmological Gravities' as higher-curvature theories in D≥3 whose FLRW background equations remain second-order in derivatives. It constructs explicit examples to all curvature orders, identifies theories admitting non-hairy Schwarzschild generalizations with at most second-order equations, and claims that the linearized equations for scalar cosmological perturbations in any such theory contain no more than two time derivatives (explicitly checked in 4D examples up to fifth order).

Significance. If the central perturbation result holds, the work would be significant for modified gravity: it would show that higher-curvature terms can be added while preserving second-order dynamics in the scalar cosmological sector, potentially avoiding Ostrogradsky instabilities without restricting to Einstein gravity. The all-order constructions and the non-hairy black-hole examples would also provide concrete tools for further study.

major comments (1)
  1. [Abstract] Abstract: the central claim that the second-order FLRW background condition forces the linearized scalar perturbation equations to contain at most two time derivatives is stated without any derivation or explicit general construction of Cosmological Gravity, so the load-bearing step cannot be checked.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their report. We address the single major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that the second-order FLRW background condition forces the linearized scalar perturbation equations to contain at most two time derivatives is stated without any derivation or explicit general construction of Cosmological Gravity, so the load-bearing step cannot be checked.

    Authors: The abstract is a concise summary. The manuscript first constructs explicit examples of Cosmological Gravities (theories whose FLRW equations are at most second order) to all curvature orders in D≥3. It then derives that this background condition implies the linearized scalar perturbation equations contain at most two time derivatives for any such theory in D≥3. The general argument appears in the main text; explicit verification is given by computing the perturbation equations for four-dimensional examples up to fifth order. The load-bearing step is therefore presented for checking in the body of the paper. revision: no

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

Only the abstract is available. It defines Cosmological Gravities by the property that their FLRW background equations are second-order in derivatives, then states as a derived result that scalar perturbations in any such theory (D≥3) have at most two time derivatives. No equations, explicit constructions, or self-citations are supplied that would allow exhibition of a reduction by construction, fitted input, or load-bearing self-reference. The claim is presented as an investigated finding rather than a definitional equivalence or renamed input, so the derivation chain cannot be shown to collapse.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no information on free parameters, axioms, or invented entities.

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Forward citations

Cited by 1 Pith paper

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  1. Cosmic Inflation From Regular Black Holes

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    Regular black holes in the bulk of quasi-topological gravity drive a de Sitter inflationary phase on the brane at small scales, with e-fold number set by the ratio of black hole radius to higher-curvature scale.

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