Variational and conformal structure of nonlinear metric-connection gravitational Lagrangians

Cotsakis, Spiros; Miritzis, John; Querella, Laurent

doi:10.1063/1.532744

Cited by 31 publications

(47 citation statements)

References 23 publications

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“…The resulting theory is then general relativity with its Riemannian geometry, but actually one is implicitly dealing with much broader geometrical setting. To some authors, this has implied a strong objection against the "Palatini's device" in general 4 [28,29,30,31]. However, this issue is simply avoided if one regards the spacetime as Riemannian from the beginning.…”

Section: A Consequences and Interpretations Of The Resultsmentioning

confidence: 99%

“…Our derivations generalize theirs.) Furthermore, the essentially problematic role of the independent connection in the Palatini formulation [28,29], first pointed out in the early works by Buchdahl [30,31], has gone largely unrecognized in the recent literature 1 . We find it worthwhile to consider in detail some of these rather fundamental aspects of the structure of these theories.…”

Section: Introductionmentioning

confidence: 99%

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A note on covariant conservation of energy–momentum in modified gravities

Koivisto¹

2006

Class. Quantum Grav.

378

308

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An explicit proof of the vanishing of the covariant divergence of the energy-momentum tensor in modified theories of gravity is presented. The gravitational action is written in arbitrary dimensions and allowed to depend nonlinearly on the curvature scalar and its couplings with a scalar field. Also the case of a function of the curvature scalar multiplying a matter Lagrangian is considered. The proof is given both in the metric and in the first-order formalism, i.e. under the Palatini variational principle. It is found that the covariant conservation of energy-momentum is built-in to the field equations. This crucial result, called the generalized Bianchi identity, can also be deduced directly from the covariance of the extended gravitational action. Furthermore, we demonstrate that in all of these cases, the freely falling world lines are determined by the field equations alone and turn out to be the geodesics associated with the metric compatible connection. The independent connection in the Palatini formulation of these generalized theories does not have a similar direct physical interpretation. However, in the conformal Einstein frame a certain bi-metricity emerges into the structure of these theories. In the light of our interpretation of the independent connection as an auxiliary variable we can also reconsider some criticisms of the Palatini formulation originally raised by Buchdahl.

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Section: A Consequences and Interpretations Of The Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A note on covariant conservation of energy–momentum in modified gravities

Koivisto¹

2006

Class. Quantum Grav.

378

308

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“…ρσ term was already established in literature [8,34]. And now we will calculate the actual difference at the level of solutions, expanding the equations in powers of λ.…”

Section: The Fact That F1 and F2 Versions Of Einstein Equation Differmentioning

confidence: 99%

Comparing metric and Palatini approaches to vector Horndeski theory

Давыдов

2018

Int. J. Mod. Phys. D

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We compare cosmologic and spherically symmetric solutions to metric and Palatini versions of vector Horndeski theory. It appears that Palatini formulation of the theory admits more degrees of freedom. Specifically, homogeneous isotropic configuration is effectively bimetric, and static spherically symmetric configuration contains non-metric connection. In general, the exact solution in metric case coincides with the approximative solution in Palatini case. The Palatini version of the theory appears to be more complicated, but the resulting non-linearity may be useful: we demonstrate that it allows the specific cosmological solution to pass through singularity, which is not possible in metric approach.

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“…eqs (30) and (31) in [28]). More general Lagrangians have also been suggested, especially in the context of the Palatini formalism, for example L = e −φ R in [29]; L = R + βR 2 − 2Λ gravity for FRW models was investigated in [30]; see also [31] for a formulation of a theory invariant with respect to Weyl transformations and [32] for the inclusion of torsion.…”

Section: A Simple Lagrangianmentioning

confidence: 99%