Noether Symmetries in Theories of Gravity

Bajardi, F; Capozziello, Salvatore

doi:10.1017/9781009208727

Cited by 20 publications

(13 citation statements)

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“…leave the gravitational action (2.14) unchanged, δS g = 0, and the domain of integration Ω can be chosen arbitrarily, by means of the variation (2.30) and the assumption that the metric tensor g µν is solution of the field equations in vacuum (2.34), we find a conserved current J σ , i.e., the Noether current [43], which reads as…”

Section: Gravitational Energy-momentum Pseudotensor In Non-local Gravitymentioning

confidence: 99%

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Energy-Momentum Complex in Higher Order Curvature-Based Local Gravity

2022

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An unambiguous definition of gravitational energy remains one of the unresolved issues of physics today. This problem is related to the non-localization of gravitational energy density. In General Relativity, there have been many proposals for defining the gravitational energy density, notably those proposed by Einstein, Tolman, Landau and Lifshitz, Papapetrou, Møller, and Weinberg. In this review, we firstly explored the energy–momentum complex in an nth order gravitational Lagrangian L=Lgμν,gμν,i1,gμν,i1i2,gμν,i1i2i3,⋯,gμν,i1i2i3⋯in and then in a gravitational Lagrangian as Lg=(R¯+a0R2+∑k=1pakR□kR)−g. Its gravitational part was obtained by invariance of gravitational action under infinitesimal rigid translations using Noether’s theorem. We also showed that this tensor, in general, is not a covariant object but only an affine object, that is, a pseudo-tensor. Therefore, the pseudo-tensor ταη becomes the one introduced by Einstein if we limit ourselves to General Relativity and its extended corrections have been explicitly indicated. The same method was used to derive the energy–momentum complex in fR gravity both in Palatini and metric approaches. Moreover, in the weak field approximation the pseudo-tensor ταη to lowest order in the metric perturbation h was calculated. As a practical application, the power per unit solid angle Ω emitted by a localized source carried by a gravitational wave in a direction x^ for a fixed wave number k under a suitable gauge was obtained, through the average value of the pseudo-tensor over a suitable spacetime domain and the local conservation of the pseudo-tensor. As a cosmological application, in a flat Friedmann–Lemaître–Robertson–Walker spacetime, the gravitational and matter energy density in f(R) gravity both in Palatini and metric formalism was proposed. The gravitational energy–momentum pseudo-tensor could be a useful tool to investigate further modes of gravitational radiation beyond two standard modes required by General Relativity and to deal with non-local theories of gravity involving □−k terms.

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Section: Gravitational Energy-momentum Pseudotensor In Non-local Gravitymentioning

confidence: 99%

“…Here, we want to propose a generalization of Einstein gravitational pseudotensor to non-local gravity models involving f ( −1 ) operators. It will be derived from a variational principle using the Noether theorem applied to a gravitational Lagrangian invariant under global translations [43]. This object remains an affine tensor, i.e.…”

Section: Introductionmentioning

confidence: 99%

Energy-Momentum Complex in Higher Order Curvature-Based Local Gravity

2022

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“…This class of gravitational models also satisfies the parameterized post-Newtonian observational constraints [70] for a large number of models. The teleparallel analogue of Horndeski gravity also produces a number of interesting cosmologies such as those which are well-tempered [71,72], as well as those that are derived from Noether symmetry considerations [73][74][75][76][77]. In this way, all models that were previously disqualified in regular Horndeski may be revived in this new formalism based on TG.…”

Section: Introductionmentioning

confidence: 99%

Ghost and Laplacian instabilities in teleparallel Horndeski gravity

Capozziello¹,

Caruana²,

Said³

et al. 2023

J. Cosmol. Astropart. Phys.

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Teleparallel geometry offers a platform on which to build up theories of gravity where torsion rather than curvature mediates gravitational interaction. The teleparallel analogue of Horndeski gravity is an approach to teleparallel geometry where scalar-tensor theories are considered in this torsional framework. Teleparallel gravity is based on the tetrad formalism. This turns out to result in a more general formalism of Horndeski gravity. In other words, the class of teleparallel Horndeski gravity models is much broader than the standard metric one. In this work, we explore constraints on this wide range of models coming from ghost and Laplacian instabilities. The aim is to limit pathological branches of the theory by fundamental considerations. It is possible to conclude that a very large class of models results physically viable.

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“…The issues of causality, domain of validity and boundary conditions in non-local classical and quantum field theories have been discussed [28,30], and in both cases, physically viable models can be constructed. In recent years, we have seen a great interest in phenomenological aspects of nonlocal gravity models [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Structure formation in non-local bouncing models

Jackson

Bufalo

2023

J. Cosmol. Astropart. Phys.

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In this study, we investigate the growth of structures within the Deser-Woodard nonlocal theory and extend it to various bouncing cosmology scenarios. Our findings show that the observable structure growth rate, fσ 8, in a vacuum-dominated universe is finite within the redshift range of 0 < z < 2, contrary to previous literature. Although fσ 8 exhibits no divergences, we observe a slight difference between the evolution of the ΛCDM and the non-local DW II models. Regarding structure formation in bouncing cosmologies, we evaluate the evolution of fσ 8 near the bouncing point. Among the different bouncing cases we explore, the oscillatory bounce and pre-inflationary asymmetrical bounce demonstrate a physical profile where the growth rate begins as a small perturbation in the early epoch and increases with inflation, which can be regarded as the seeds of large-scale structures. These findings are significant because they shed light on the growth of seed fluctuations into cosmic structures resulting from non-local effects.

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Noether Symmetries in Theories of Gravity

Cited by 20 publications

References 0 publications

Energy-Momentum Complex in Higher Order Curvature-Based Local Gravity

Energy-Momentum Complex in Higher Order Curvature-Based Local Gravity

Ghost and Laplacian instabilities in teleparallel Horndeski gravity

Structure formation in non-local bouncing models

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