Linear Weyl gravity in de Sitter universe

Takook, M. V.; Tanhayi, Mohammad Reza

doi:10.1007/jhep12(2010)044

Cited by 21 publications

(25 citation statements)

References 56 publications

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“…The d'Alembertian operator becomes [40] 35) where, the conditions of tracelessness and divergence free (e.i.∂.K = 0 = K ), have been imposed to the physical states. By use of the above equations in eq.…”

Section: Jhep03(2016)203mentioning

confidence: 99%

Group theoretical interpretation of the modified gravity in de Sitter space

Dehghani

2016

J. High Energ. Phys.

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A framework has been presented for theoretical interpretation of various modified gravitational models which is based on the group theoretical approach and unitary irreducible representations (UIR's) of de Sitter (dS) group. In order to illustrate the application of the proposed method, a model of modified gravity has been investigated. The background field method has been utilized and the linearized modified gravitational field equation has been obtained in the 4-dimensional dS space-time as the background. The field equation has been written as the eigne-value equation of the Casimir operators of dS space using the flat 5-dimensional ambient space notations. The Minkowskian correspondence of the theory has been obtained by taking the zero curvature limit. It has been shown that under some simple conditions, the linearized modified field equation transforms according to two of the UIR's of dS group labeled by Π ± 2,1 and Π ± 2,2 in the discrete series. It means that the proposed modified gravitational theory can be a suitable one to describe the quantum gravitational effects in its linear approximation on dS space. The field equation has been solved and the solution has been written as the multiplication of a symmetric rank-2 polarization tensor and a massless scalar field using the ambient space notations. Also the two-point function has been calculated in the ambient space formalism. It is dS invariant and free of any theoretical problems.

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Section: Jhep03(2016)203mentioning

confidence: 99%

Group theoretical interpretation of the modified gravity in de Sitter space

Dehghani

2016

J. High Energ. Phys.

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“…In this case, the covariant derivatives in de Sitter intrinsic space are related to the derivative in embedding space as [43] …”

Section: Two-point Functions In Intrinsic Coordinatesmentioning

confidence: 99%

Conformally covariant vector–spinor field in de Sitter space

2014

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In this paper, we study conformally invariant field equations for a vector-spinor spin− 3 2 field in the de Sitter space-time. The solutions are also obtained in terms of the de Sitter-Dirac plane waves. The related two-point functions are calculated in both the de Sitter ambient space formalism and intrinsic coordinates. In order to study the conformal invariance, Dirac's six-cone formalism is utilized in which the field equations are expressed in a manifestly conformal way in 4+2-dimensional conformal space and then followed by a projection to the de Sitter space.

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“…The other part is a spin-2 conformal field, which propagates on the dS background space time and it is a massless conformal quantum field [24]. From the group theoretical point of view it is proved that the second part cannot be described by a rank-2 symmetric tensor field in the ambient space notation or Dirac 6 -cone formalism [58][59][60]. It must be chosen as a spin-2 rank-3 mixed symmetric tensor field K αβγ , which simultaneously transforms under the dS and conformal groups.…”

Section: Entropy In De Sitter Space-timementioning

confidence: 99%

“…Such a field is supposed to transform simultaneously under the unitary irreducible representation (UIR) of the dS group and the conformal group SO (2,4) . The rank-2 symmetric tensor field K αβ (linear gravity) in the ambient space notation (or in the Dirac's 6 -cone formalism) cannot be transformed simultaneously under the UIR of the dS and the conformal groups [58][59][60]. The linear gravity (or the conformal gauge gravity in the dS background), which transforms simultaneously under the UIR of the dS and the conformal groups, is a spin-2 rank-3 mixed symmetry tensor field K αβγ [24,[59][60][61].…”

Section: Introductionmentioning

confidence: 99%

“…The rank-2 symmetric tensor field K αβ (linear gravity) in the ambient space notation (or in the Dirac's 6 -cone formalism) cannot be transformed simultaneously under the UIR of the dS and the conformal groups [58][59][60]. The linear gravity (or the conformal gauge gravity in the dS background), which transforms simultaneously under the UIR of the dS and the conformal groups, is a spin-2 rank-3 mixed symmetry tensor field K αβγ [24,[59][60][61]. This field is also gauge invariant and then it corresponds to the indecomposable representation of the dS group, though its physical states (or central parts) correspond to the lowest representation of the discrete series of the dS and the conformal groups [24].…”

Section: Introductionmentioning

confidence: 99%

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Entropy of massive quantum fields in de Sitter space–time

Takook

2016

Annals of Physics

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The quantum states or Hilbert spaces for the quantum field theory in de Sitter space-time are studied on ambient space formalism. In this formalism, the quantum states are only depended (1) on the topological character of the de Sitter space-time, i.e. IR × S 3 , and (2) on the homogeneous spaces which are used for construction of the unitary irreducible representation of de Sitter group. A compact homogeneous space is chosen in this paper. The unique feature of this homogeneous space is that its total number of quantum states, N , is finite although the Hilbert space has infinite dimensions. It is shown that N is a continuous function of the Hubble constant H and the eigenvalue of the Casimir operators of de Sitter group. The entropy of the quantum fields on this Hilbert space have been calculated which is finite and invariant for all inertial observers on the de Sitter hyperboloid.

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Linear Weyl gravity in de Sitter universe

Cited by 21 publications

References 56 publications

Group theoretical interpretation of the modified gravity in de Sitter space

Group theoretical interpretation of the modified gravity in de Sitter space

Conformally covariant vector–spinor field in de Sitter space

Entropy of massive quantum fields in de Sitter space–time

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