Palatini variational principle for an extended Einstein-Hilbert action

Burton, Howard; Mann, Robert B.

doi:10.1103/physrevd.57.4754

Cited by 20 publications

(28 citation statements)

References 9 publications

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“…This seems indeed like a precarious balance, so we might be tempted to give up any hope of generalizing the Levi-Civita condition. 3 But motivated by the fact that the relationship between 1 I thank M. S. Narasimhan for pointing out that the higher tensor idea dates back to Riemann. 2 This is an assumption we will make throughout the paper.…”

Section: Ingredientsmentioning

confidence: 98%

A Generalization of Gravity

Krishnan

2015

Found Phys

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I consider theories of gravity built not just from the metric and affine connection, but also other (possibly higher rank) symmetric tensor(s). The Lagrangian densities are scalars built from them, and the volume forms are related to Cayley's hyperdeterminants. The resulting diff-invariant actions give rise to geometric theories that go beyond the metric paradigm (even metric-less theories are possible), and contain Einstein gravity as a special case. Examples contain theories with generalizeations of Riemannian geometry. The 0-tensor case is related to dilaton gravity. These theories can give rise to new types of spontaneous Lorentz breaking and might be relevant for "dark" sector cosmology.

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Section: Ingredientsmentioning

confidence: 98%

A Generalization of Gravity

Krishnan

2015

Found Phys

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“…Assuming a symmetric metric and a symmetric connection it is straightforward to perform a Palatini variation by varying the connection, compare [4] equation (8) δΓ μν…”

Section: The Jordan Framementioning

confidence: 99%

“…Applying the Palatini variation to the Jordan frame gives a non-metric connection. The only place where Palatini variation of the Jordan frame is looked at is in [4,5] ; however there it is not explicitly stated that the existence of a dilaton forces the geometry of spacetime to be a Weyl geometry, which was suggested on string theory grounds in [23] . There are usually considered to be two types of frame: the Jordan frame and the Einstein frame; perhaps because of the geometry involved it is better to call the Jordan frame with non-metricity the Weyl frame.…”

Section: Introductionmentioning

confidence: 99%

Is Spacetime Non-metric?

Roberts¹

2018

Expert Opin Astron Astrophys

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If one assumes higher dimensions and that dimensional reduction from higher dimensions produces scalar-tensor theory and also that Palatini variation is the correct method of varying scalar-tensor theory then spacetime is nonmetric. Palatini variation of Jordan frame lagrangians gives an equation relating the dilaton to the object of non-metricity and hence the existence of the dilaton implies that the spacetime connection is more general than that given soley by the Christoffel symbol of general relativity. Transferring from Jordan to Einstein frame, which connection, lagrangian, field equations and stress conservation equations occur are discussed: it is found that the Jordan frame has more information, this can be expressed in several ways, the simplest is that the extra information corresponds to the function multiplying the Ricci scalar in the action. The Einstein frame has the advantages that stress conservation implies no currents and that the field equations are easier to work with. This is illustrated by application to Robertson-Walker spacetime.

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“…A geometrical approach to theories with non-minimal coupling is particularly interesting. According to it, by considering the Palatini variational method a not necessarily Riemannian compatibility condition between the metric tensor and the affine connection-initially taken as independent variables-is obtained [9,10]. Furthermore, it was shown that the geometry that naturally appears when a symmetric affine connection is regarded is the so called integrable Weyl geometry, where the scalar field takes part together with the metric tensor in the description of the gravitational field.…”

Section: Introductionmentioning

confidence: 99%

Cosmological Solutions for the Geometrical Scalar-Tensor with the Potential Determined by the Noether Symmetry Approach

Barreto

Kremer

2020

Symmetry

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The aim of this work is to study a scalar-tensor theory where owing to Palatini’s variational method the space-time is endowed with a geometrical structure of Weyl integrable type. The geometrical nature of the scalar field is related to the non-metricity so that the theory is known as geometrical scalar-tensor. On the framework of Weyl transformations, a non-minimally coupled scalar-tensor theory on the Jordan frame corresponds to a minimally coupled Einstein–Hilbert action on the Einstein frame. The scalar potential is selected by the Noether symmetry approach in order to obtain conserved quantities for the FRW cosmological model. Exact solutions are obtained and analyzed in the context of the cosmological scenarios consistent with an expanding universe. A particular case is matched in each frame and the role of scalar field as a dark energy component is discussed.

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Palatini variational principle for an extended Einstein-Hilbert action

Cited by 20 publications

References 9 publications

A Generalization of Gravity

A Generalization of Gravity

Is Spacetime Non-metric?

Cosmological Solutions for the Geometrical Scalar-Tensor with the Potential Determined by the Noether Symmetry Approach

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