Non-Trivial Vacua in Higher-Derivative Gravitation

Ahmed Hindawi; Burt A. Ovrut; Daniel Waldram

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Non-Trivial Vacua in Higher-Derivative Gravitation

Ahmed Hindawi, Burt A. Ovrut, Daniel Waldram

High Energy Physics - Theory · Submitted 26 Sep 1995

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim For general fourth-order theories, described by actions which are general functions of the scalar curvature, the Ricci tensor and the full Riemann tensor, it is shown that the higher-derivative theories may have multiple stable vacua.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.06 · mentions code or data availability 0.01.

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arXiv listing abstract v3. Results and the main claim are underlined; show every role.

A discussion of an extended class of higher-derivative classical theories of gravity is presented. A procedure is given for exhibiting the new propagating degrees of freedom, at the full non-linear level, by transforming the higher-derivative action to a canonical second-order form. For general fourth-order theories, described by actions which are general functions of the scalar curvature, the Ricci tensor and the full Riemann tensor, it is shown that the higher-derivative theories may have multiple stable vacua. The vacua are shown to be, in general, non-trivial, corresponding to deSitter or anti-deSitter solutions of the original theory. It is also shown that around any vacuum the elementary excitations remain the massless graviton, a massive scalar field and a massive ghost-like spin-two field. The analysis is extended to actions which are arbitrary functions of terms of the form $\nabla^{2k}R$, and it is shown that such theories also have a non-trivial vacuum structure.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	A discussion of an extended class of higher-derivative classical theories of gravity is presented.	contribution 0.79	0.76	0.04	asserted 0.71
s1	A procedure is given for exhibiting the new propagating degrees of freedom, at the full non-linear level, by transforming the higher-derivative action to a canonical second-order form.	method 0.98	0.91	0.07	asserted 0.99
s2	For general fourth-order theories, described by actions which are general functions of the scalar curvature, the Ricci tensor and the full Riemann tensor, it is shown that the higher-derivative theories may have multiple stable vacua.	result 0.99	0.91	0.43	hedged possibility 0.81
s3	The vacua are shown to be, in general, non-trivial, corresponding to deSitter or anti-deSitter solutions of the original theory.	result 0.95	0.91	0.28	asserted 1.00
s4	It is also shown that around any vacuum the elementary excitations remain the massless graviton, a massive scalar field and a massive ghost-like spin-two field.	result 1.00	0.91	0.15	asserted 1.00
s5	The analysis is extended to actions which are arbitrary functions of terms of the form $\nabla^{2k}R$, and it is shown that such theories also have a non-trivial vacuum structure.	result 0.52	0.92	0.16	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 1.00.

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The paper

Original abstract

A discussion of an extended class of higher-derivative classical theories of gravity is presented. A procedure is given for exhibiting the new propagating degrees of freedom, at the full non-linear level, by transforming the higher-derivative action to a canonical second-order form. For general fourth-order theories, described by actions which are general functions of the scalar curvature, the Ricci tensor and the full Riemann tensor, it is shown that the higher-derivative theories may have multiple stable vacua. The vacua are shown to be, in general, non-trivial, corresponding to deSitter or anti-deSitter solutions of the original theory. It is also shown that around any vacuum the elementary excitations remain the massless graviton, a massive scalar field and a massive ghost-like spin-two field. The analysis is extended to actions which are arbitrary functions of terms of the form $\nabla^{2k}R$, and it is shown that such theories also have a non-trivial vacuum structure.

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References

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Cited by 6 Pith papers

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Elementary-Symmetric Ricci Gravity: Metric Formulation
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A Lagrangian built from elementary symmetric polynomials of the Ricci tensor yields multibranch vacua and a cosmological transition between de Sitter attractors.
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hep-th 2025-06 conditional novelty 6.0 of 10

For d>4, pure R^{d/2} gravity has no modes on flat space, and five-dimensional conformal gravity propagates three scalar, three vector, and two tensor modes, one of which is a ghost.
Constraining f(R) Gravity as a Scalar Tensor Theory
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Viable f(R) gravity models that pass solar system tests cannot produce dark energy distinguishable from a cosmological constant, whether they hide the scalar via large mass or via the chameleon effect.
Higher Curvature Gravity in TeV-Scale Extra Dimensions
hep-ph 2006-03 conditional novelty 6.0 of 10

For general F(R,P,Q) gravity, ADD and RS collider signatures remain qualitatively intact but gain O(1) rescalings and new heavy scalar KK towers.

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Universal Nonminimal Coupling-to-Starobinsky Matching and a Single-Field Attractor
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A claimed off-shell commutativity theorem in quadratic gravity is used to match generic nonminimal couplings to a Starobinsky R^2 sector and to derive a selection-enhanced single-field attractor bound, but the central...

How the literature uses it

15 arXiv papers cite this in 34 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 25 sentences without a confident label

Uses its method or tool 1 paper

Following the steps in Refs. [ref] , we perform an expansion of Eq. [ref] up to second order in curvature invariants around a MS solution to study the excitations of the theory around such background.

Higher-order theories of gravity: diagnosis, extraction and reformulation via non-metric extra degrees of freedom · The expansion procedure · 1.00

Compares with it 1 paper

Then it can be shown that at the bilinear level the linearisation of the theory over a maximally symmetric spacetime will be the same as the theory obtained in [ref] ,

Generalized modified gravity with the second order acceleration equation · weak field limit · 0.87

Cites it as support 2 papers

Assuming auxiliary fields enter algebraically and $f”(R)>0$, these operations commute at the action level; any ordering yields the same reduced bulk action up to total–derivative boundary terms (Fig. [ref]) [ref] .

Universal Nonminimal Coupling-to-Starobinsky Matching and a Single-Field Attractor · Off–shell commutativity and universality · 0.96
Regarding these kinds of corrections, it has been shown, both at the level of the equations of motion [ref] , and of the action [ref] , that an ETG of the type [equation] can in general be rewritten as a theory describing a set of scalar fields non-minimally coupled to standard GR.

Higher-order theories of gravity: diagnosis, extraction and reformulation via non-metric extra degrees of freedom · General higher-order theories · 0.98

Cites it as background 3 papers

More generally, the global stability (i.e., the absence of runaway solutions) and the local stability (i.e., the identification of Lyapunov stable vacua) of Quadratic Gravity are yet to be determined, see also [ref] .

Nonlinear Evolution of Quadratic Gravity in 3+1 Dimensions · Outlook · 0.92
This method has been widely used in many contexts [ref] .

Higher-order theories of gravity: diagnosis, extraction and reformulation via non-metric extra degrees of freedom · Auxiliary fields method · 0.80
Perhaps the most fruitful area of their application is cosmology, e.g. in [ref] , where the scalar field is often employed as a quintessence field to drive accelerating phases of the universe; scalar-tensor theories naturally appear in brane-world scenarios [ref] , or arise as equivalent formulations of $f(R)$ gravity theories with Ricci scalar corrections [ref] .

Brans-Dicke geometry · Introduction · 0.98

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