Do non-linear metric theories of gravitation really exist?

Ferraris, Maurizio; Francaviglia, M.; Magnano, Guido

doi:10.1088/0264-9381/5/6/002

Cited by 69 publications

(46 citation statements)

References 9 publications

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“…In summary, a fourth-order theory is conformally equivalent to the standard second-order Einstein theory plus a scalar field (see also [26,27]). If the theory is higher than fourth order, we have Lagrangian densities of the form [28][29][30],…”

Section: Conformal Transformations and Higher-order Gravitymentioning

confidence: 99%

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Galaxy rotation curves inf(R,ϕ)gravity

Stabile

Capozziello

2013

Phys. Rev. D

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We investigate the possibility to explain theoretically the galaxy rotation curves by a gravitational potential in total absence of dark matter. To this aim an analytic fourth-order theory of gravity, nonminimally coupled with a massive scalar field is considered. Specifically, the interaction term is given by an analytic function f (R, φ) where R is the Ricci scalar and φ is the scalar field. The gravitational potential is generated by a point-like source and compared with the so called Sanders's potential that can be exactly reproduced in this case. This result means that the problem of dark matter in spiral galaxies could be fully addressed by revising general relativity at galactic scales and requiring further gravitational degrees of freedom instead of new material components that have not been found out up to now.

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Section: Conformal Transformations and Higher-order Gravitymentioning

confidence: 99%

“…It is evident that the trace equation (the fourth in the system (27)), provides a differential equation with respect to the Ricci scalar which allows to solve exactly the system (27) at O(1) -order. Finally, one gets the general solution :…”

Section: A Yukawa-like Corrections In F (R)-gravitymentioning

confidence: 99%

Galaxy rotation curves inf(R,ϕ)gravity

Stabile

Capozziello

2013

Phys. Rev. D

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“…Regarding the dynamical field content of the theory, the fact that quadratic corrections to the Einstein-Hilbert action introduce a massive scalar field was noted in (Buchbinder et al, 1992;Stelle, 1978Stelle, , 1977Strominger, 1984;Utiyama and DeWitt, 1962;Vilkovisky, 1992); this applies to any f (R) gravity theory in the metric formalism [see, e.g., (Ferraris et al, 1988;Hindawi et al, 1996;Olmo, 2007)]. The metric tensor contains, in principle, various degrees of freedom: spin 2 modes, and vector and scalar modes, which can all be massless or massive.…”

Section: Metric F (R) Gravitymentioning

confidence: 99%

“…Due to the Gauss-Bonnet identity, one can reduce the theory under consideration to 22 f (R, R µν R µν ) which, in general, contains a massive spin 2 ghost field in addition to the usual massless graviton and the massive scalar. f (R) theories have no ghosts (Buchbinder et al, 1992;Ferraris et al, 1988;Stelle, 1978Stelle, , 1977Strominger, 1984;Utiyama and DeWitt, 1962;Vilkovisky, 1992), and the stability condition f ′′ (R) ≥ 0 of (Dolgov and Kawasaki, 2003a;Faraoni, 2006a) essentially amounts to guarantee that the scalaron is not a ghost. Theories of the kind f (R, R µν R µν , R µνρσ R µνρσ ) in general are plagued by ghosts [this is the case, for example, of conformal gravity, as noticed long before the 1998 discovery of the cosmic acceleration (Riegert, 1984)], but models with only f R, R 2 − 4R µν R µν + R µνρσ R µνρσ terms in the action are ghost-free (Comelli, 2005;Navarro and Van Acoleyen, 2006).…”

Section: Ghost Fieldsmentioning

confidence: 99%

Metric-affine f(R) theories of gravity

2007

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Modified gravity theories have received increased attention lately due to combined motivation coming from high-energy physics, cosmology and astrophysics. Among numerous alternatives to Einstein's theory of gravity, theories which include higher order curvature invariants, and specifically the particular class of f (R) theories, have a long history. In the last five years there has been a new stimulus for their study, leading to a number of interesting results. We review here f (R) theories of gravity in an attempt to comprehensively present their most important aspects and cover the largest possible portion of the relevant literature. All known formalisms are presentedmetric, Palatini and metric-affine -and the following topics are discussed: motivation; actions, field equations and theoretical aspects; equivalence with other theories; cosmological aspects and constraints; viability criteria; astrophysical applications.

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“…Under suitable regularity conditions on the Lagrangian and using a Legendre transformation on the metric, higher order theories take the form of GR in which one or more scalar field(s) source of the gravitational field (see, e .g., [9,[57][58][59]). On the other hand, as discussed above, the mathematical equivalence between models with variable gravitational coupling and Einstein gravity has been studied using suitable conformal transformations [60,61].…”

Section: Introductionmentioning

confidence: 99%

A Bird's Eye View of f (R)-Gravity

Capozziello¹,

Laurentis²,

Faraoni³

2010

TOAAJ

112

135

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Abstract:The currently observed accelerated expansion of the Universe suggests that cosmic flow dynamics is dominated by some unknown form of dark energy characterized by a large negative pressure. This picture comes out when such a new ingredient, beside baryonic and dark matter, is considered as a source in the r.h.s. of the field equations. Essentially, it should be some form of un-clustered, non-zero vacuum energy which, together with (clustered) dark matter, should drive the global cosmic dynamics. Among the proposals to explain the experimental situation, the "concordance model", addressed as ! CDM, gives a reliable snapshot of the today observed Universe according to the CMBR, LSS and SNeIa data, but presents dramatic shortcomings as the "coincidence and cosmological constant problems" which point out its inadequacy to fully trace back the cosmological dynamics. On the other hand, alternative theories of gravity, extending in some way General Relativity, allow to pursue a different approach giving rise to suitable cosmological models where a late-time accelerated expansion can be achieved in several ways. This viewpoint does not require to find out candidates for dark energy and dark matter at fundamental level (they have not been detected up to now), it takes into account only the "observed" ingredients (i.e. gravity, radiation and baryonic matter), but the l.h.s. of the Einstein equations has to be modified. Despite of this modification, it could be in agreement with the spirit of General Relativity since the only request is that the Hilbert-Einstein action should be generalized asking for a gravitational interaction acting, in principle, in different ways at different scales. We survey the landscape of ) (R f theories of gravity in their various formulations, which have been used to model the cosmic acceleration as alternatives to dark energy and dark matter. Besides, we take into account the problem of gravitational waves in such theories. We discuss some successes of ) (R f -gravity (whereis a generic function of Ricci scalar R ), theoretical and experimental challenges that they face in order to satisfy minimal criteria for viability.

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Do non-linear metric theories of gravitation really exist?

Cited by 69 publications

References 9 publications

Galaxy rotation curves inf(R,ϕ)gravity

Galaxy rotation curves inf(R,ϕ)gravity

Metric-affine f(R) theories of gravity

A Bird's Eye View of f (R)-Gravity

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