Scale Transformations in Metric-Affine Geometry

Iosifidis, Damianos; Koivisto, Tomi S.

doi:10.3390/universe5030082

Cited by 77 publications

(124 citation statements)

References 94 publications

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“…All of these spaces are representations of SO(d−1), some irreducible and others not. In order to obtain the irreps, let us note that the hs-and ha-projections of 3 2 LT T and T T L+T LT − 1 2 LT T are themselves projectors. Finally, in several of these representations one can isolate the "trace" and the "tracefree" part.…”

Section: Gl(d)-decompositionmentioning

confidence: 99%

“…In the literature, more attention has been given to theories with torsion, but recently there has been a great deal of interest for MAGs with non-metricity, see e.g. [3][4][5][6][7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

“…It is thus of obvious interest to determine what special classes of MAGs could be free of ghosts and tachyons. In the metric case, the most general ghost and tachyon-free theories not containing accidental symmetries 3 have been determined in [28,29]. It was based on the use of spin projectors for a general two-index tensor and a three-index tensor, antisymmetric in one pair.…”

Section: Introductionmentioning

confidence: 99%

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New class of ghost- and tachyon-free metric affine gravities

2020

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We construct the spin-projection operators for a theory containing a symmetric two-index tensor and a general three-index tensor. We then use them to analyse, at linearized level, the most general action for a metric-affine theory of gravity with terms up to second order in curvature, which depends on 28 parameters. In the metric case we recover known results. In the torsion-free case, we are able to determine the most general six-parameter class of theories that are projective invariant, contain only one massless spin 2 and no spin 3, and are free of ghosts and tachyons.1 By quadratic gravity we mean theories with action containing terms linear and quadratic in the Riemann tensor.2 As an example let us mention here Weyl geometry, where φ is constructed in terms of a vector field. This theory has been revisited recently in [27].3 By accidental symmetry we mean a gauge symmetry that is present in the linearized action but not in the full action 4 This is due to the use of the vierbein formalism. The general two-index tensor is the linearized vierbein and the three-index tensor is the linearized spin connection.

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Section: Gl(d)-decompositionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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New class of ghost- and tachyon-free metric affine gravities

2020

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“…Finally, we discuss the applications of the Theorem in Metric-Affine Gravity and we show how it can be used to derive invariant Gravity actions under connection transformations. In particular we reproduce the results for the projective invariant quadratic (in torsion and non-metricity) action of [17] and we also derive the constraints for an enhanced invariance. We then conclude our results and also discuss other possible applications.…”

Section: Introductionmentioning

confidence: 80%

“…We will now show how one can restrict the parameter space in order to obtain a projective invariant Theory without computing the change in S directly but by simply looking at its Γ-variation. Indeed, varying the above with respect to the connection, we have [17] Ψ µν…”

Section: Applications To Gravitymentioning

confidence: 99%

Linear transformations on affine-connections

Iosifidis

2020

Class. Quantum Grav.

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We state and prove a simple Theorem that allows one to generate invariant quantities in Metric-Affine Geometry, under a given transformation of the affine connection. We start by a general functional of the metric and the connection and consider transformations of the affine connection possessing a certain symmetry. We show that the initial functional is invariant under the aforementioned group of transformations iff its Γ-variation produces tensor of a given symmetry. Conversely if the tensor produced by the Γ-variation of the functional respects a certain symmetry then the functional is invariant under the associated transformation of the affine connection. We then apply our results in Metric-Affine Gravity and produce invariant actions under certain transformations of the affine connection.

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Cosmology of Metric‐Affine R+βR2$R + \beta R^2$ Gravity with Pure Shear Hypermomentum

Iosifidis,

Myrzakulov,

Ravera

2023

Fortschritte der Physik

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In this paper, cosmological aspects of metric‐affine gravity with hyperfluid are studied. The equations of motion of the theory are obtained by varying the action with respect to the metric and the independent connection. Subsequently, considering a Friedmann‐Lemaître‐Robertson‐Walker background, the modified Friedmann equations in the presence of a perfect cosmological hyperfluid is derived. Especially, a particular case in which is focused, considering purely shear hypermomentum and finding exact solutions in the weak coupling limit.

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Scale Transformations in Metric-Affine Geometry

Cited by 77 publications

References 94 publications

New class of ghost- and tachyon-free metric affine gravities

New class of ghost- and tachyon-free metric affine gravities

Linear transformations on affine-connections

Cosmology of Metric‐Affine R+βR2$R + \beta R^2$ Gravity with Pure Shear Hypermomentum

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