Classical gravity with higher derivatives

Stelle, K.S.

doi:10.1007/bf00760427

Cited by 1,232 publications

(1,492 citation statements)

References 13 publications

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“…Models involving higher curvature invariants have been interesting to theorists since early investigations by Stelle [299,300], which showed in particular that a theory with quadratic curvature terms is renormalizable. In the context of inflation, Starobinsky wrote down a Lagrangian of the form L ∼ R + R 2 which was shown to be able to drive cosmic acceleration [301] in the early universe.…”

Section: Example: F (R) Gravitymentioning

confidence: 99%

Beyond the cosmological standard model

et al. 2015

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After a decade and a half of research motivated by the accelerating universe, theory and experiment have a reached a certain level of maturity. The development of theoretical models beyond Λ or smooth dark energy, often called modified gravity, has led to broader insights into a path forward, and a host of observational and experimental tests have been developed. In this review we present the current state of the field and describe a framework for anticipating developments in the next decade. We identify the guiding principles for rigorous and consistent modifications of the standard model, and discuss the prospects for empirical tests.We begin by reviewing recent attempts to consistently modify Einstein gravity in the infrared, focusing on the notion that additional degrees of freedom introduced by the modification must "screen" themselves from local tests of gravity. We categorize screening mechanisms into three broad classes: mechanisms which become active in regions of high Newtonian potential, those in which first derivatives of the field become important, and those for which second derivatives of the field are important. Examples of the first class, such as f (R) gravity, employ the familiar chameleon or symmetron mechanisms, whereas examples of the last class are galileon and massive gravity theories, employing the Vainshtein mechanism. In each case, we describe the theories as effective theories and discuss prospects for completion in a more fundamental theory. We describe experimental tests of each class of theories, summarizing laboratory and solar system tests and describing in some detail astrophysical and cosmological tests. Finally, we discuss prospects for future tests which will be sensitive to different signatures of new physics in the gravitational sector.The review is structured so that those parts that are more relevant to theorists vs. observers/experimentalists are clearly indicated, in the hope that this will serve as a useful reference for both audiences, as well as helping those interested in bridging the gap between them.

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Section: Example: F (R) Gravitymentioning

confidence: 99%

Beyond the cosmological standard model

et al. 2015

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“…To start with, the one-loop semiclassical corrections to the gravity action produce the form factors which have exactly the form (1.1), with the non-polynomial functions F 1,2,3 = F 1,2,3 ( /m 2 ), typically with the logarithmic asymptotics in the far UV [21,22]. The constant values of F 1,2,3 correspond to the well-known fourth-derivative models of renormalizable quantum gravity [23], with existing extensive discussion of classical properties in the literature starting from [24]. Furthermore, the polynomial form of the same functions F 1,2,3 , if being introduced into the classical action, leads to super-renormalizable models of quantum gravity [20], even if the O(R 3 ... ) and other higher-order (corresponding to the order of polynomials) terms are included.…”

Section: Jhep04(2015)098mentioning

confidence: 99%

On Newtonian singularities in higher derivative gravity models

Modesto

Netto

Shapiro

2015

J. High Energ. Phys.

112

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Abstract:We consider the problem of Newtonian singularity in the wide class of higher derivative gravity models, including the ones which are renormalizable and superrenormalizable at the quantum level. The simplest version of the singularity-free theory has four derivatives and is pretty well-known. We argue that in all cases of local higherderivative theories, when the poles of the propagator are real and simple, the singularities disappear due to the cancelation of contributions from scalar and tensor massive modes.

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“…It is known that adding terms quadratic in the curvature invariants to the Einstein-Hilbert action with a cosmological constant yields an extra scalar mode and a spin-2 mode, which is generically a ghost because of its fourth-order field equation (see [49][50][51][52]). Thus, provided we are expanding around a constant φ background, such as de Sitter space, we can directly infer that Modifed Gravity models are generically afflicted by spin-2 ghosts.…”

Section: The Physical Degrees Of Freedommentioning

confidence: 99%

Ghosts, instabilities, and superluminal propagation in modified gravity models

Felice

Hindmarsh

Trodden

2006

J. Cosmol. Astropart. Phys.

161

167

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We consider Modified Gravity models involving inverse powers of fourth-order curvature invariants.Using these models' equivalence to the theory of a scalar field coupled to a linear combination of the invariants, we investigate the properties of the propagating modes. Even in the case for which the fourth derivative terms in the field equations vanish, we find that the second derivative terms can give rise to ghosts, instabilities, and superluminal propagation speeds. We establish the conditions which the theories must satisfy in order to avoid these problems in Friedmann backgrounds, and show that the late-time attractor solutions generically exhibit superluminally propagating tensor or scalar modes. * a. de-felice@sussex.ac.uk

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Classical gravity with higher derivatives

Cited by 1,232 publications

References 13 publications

Beyond the cosmological standard model

Beyond the cosmological standard model

On Newtonian singularities in higher derivative gravity models

Ghosts, instabilities, and superluminal propagation in modified gravity models

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