Conformal linear gravity in de Sitter space II

Takook, M. V.; Pejhan, Hamed; Tanhayi, Mohammad Reza

doi:10.1140/epjc/s10052-012-2052-8

Cited by 18 publications

(23 citation statements)

References 56 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Let us first introduce a traceless and transverse tensor field K in terms of a five-dimensional constant vector Z 1 = (Z 1α ) and a scalar field φ 1 and two vector fields K and K g by putting [34,39,41,42,48,49]…”

Section: Solution To the Conformal Field Equationmentioning

confidence: 99%

See 1 more Smart Citation

Group theoretical interpretation of the modified gravity in de Sitter space

Dehghani

2016

J. High Energ. Phys.

View full text Add to dashboard Cite

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.

show abstract

Section: Solution To the Conformal Field Equationmentioning

confidence: 99%

“…Very similar to the recurrence formula (3.1) let us try the following possibility [34,39,41,42,48,49] …”

Section: The Conformal Two-point Functionmentioning

confidence: 99%

Group theoretical interpretation of the modified gravity in de Sitter space

Dehghani

2016

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…The action of Casimir operators of de Sitter group Q 1 (vector Casimir operator), Q 2 and Q 3 ) (Casimir operator for the rank-2 and rank-3 tensor field respectively) can be written in the more explicit form as [27] Q 1 K α = (Q 0 − 2)K α + 2x α ∂ · K − 2∂ α x · K, (A.1)…”

Section: Appendix A: Some Useful Relationsmentioning

confidence: 99%

Auxiliary Conformally Invariant Higher-Spin Field in de Sitter Space

Tanhayi

2015

Int J Theor Phys

View full text Add to dashboard Cite

We employ de Sitter isometry to study a mixed symmetric rank-3 tensor field in de Sitter space by finding the field equation, solution and two-point function which are conformally invariant. It is proved that such a tensor field plays a key role in conformal theory of linear gravity (Binegar et al., Phys. Rev. D 27, 2249, 1983 . In de Sitter space from the group theoretical point of view this kind of tensor could associate with two unitary irreducible representations (UIR) of the de Sitter group (Takook et al., J. Math. Phys. 51, 032503, 2010), which one representation has a flat limit, namely, in zero curvature coincides to the UIR of Poincaré group, however, the second one which is named as auxiliary field, becomes significant in the study of conformal gravity in de Sitter background. We show that the rank-3 tensor solution can be written in terms of a massless minimally coupled scalar field and also the related two-point function is a function of a massless minimally coupled scalar two-point function.

show abstract

“…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%

Entropy of massive quantum fields in de Sitter space–time

Takook

2016

Annals of Physics

View full text Add to dashboard Cite

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.

show abstract

Conformal linear gravity in de Sitter space II

Cited by 18 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

Auxiliary Conformally Invariant Higher-Spin Field in de Sitter Space

Entropy of massive quantum fields in de Sitter space–time

Contact Info

Product

Resources

About