Spontaneously broken de Sitter symmetry and the gravitational holonomy group

Stelle, K.S.; West, Peter

doi:10.1103/physrevd.21.1466

Cited by 277 publications

(504 citation statements)

References 35 publications

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“…The geometry defined by the spin connection (10) and vierbein (9), together with their curvature (11) and torsion (12), is a nonlinear Riemann-Cartan geometry [7,13]. This signifies that Poincaré transformations acting on these objects are realized nonlinearly by elements of its Lorentz subgroup.…”

Section: Cartan Geometric Structure Of Teleparallel Gravitymentioning

confidence: 99%

Dark energy as a kinematic effect

Jennen

Pereira

2016

Physics of the Dark Universe

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We present a generalization of teleparallel gravity that is consistent with local spacetime kinematics regulated by the de Sitter group S O(1, 4). The mathematical structure of teleparallel gravity is shown to be given by a nonlinear Riemann-Cartan geometry without curvature, which inspires us to build the generalization on top of a de Sitter-Cartan geometry with a cosmological function. The cosmological function is given its own dynamics and naturally emerges nonminimally coupled to the gravitational field in a manner akin to teleparallel dark energy models or scalar-tensor theories in general relativity. New in the theory here presented, the cosmological function gives rise to a kinematic contribution in the deviation equation for the world lines of adjacent free-falling particles. While having its own dynamics, dark energy manifests itself in the local kinematics of spacetime.

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Section: Cartan Geometric Structure Of Teleparallel Gravitymentioning

confidence: 99%

Dark energy as a kinematic effect

Jennen

Pereira

2016

Physics of the Dark Universe

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“…[9] is used, L G is the gravitational Lagrangian, R is the scalar curvature, Λ is the positive cosmological constant, S cab = g cd S d ab , S d ab is the torsion tensor, g cd is the metric tensor, S a = S c ac , a, b, c, etc., are abstract indices [21,22], and a 1 , a 2 , a 3 are three dimensionless parameters. The Lagrangian (1) is gauge invariant because each of the metric, torsion and curvature can be expressed in a gauge-invariant way [2][3][4][8][9][10]. Moreover, the Lagrangian is complete in the sense that it contains all components of the gravitational field strength F ab , i.e., it contains both curvature and torsion.…”

Section: R + S Theories Of Gravitymentioning

confidence: 99%

“…The spacetime torsion is introduced in the gauge theory of gravity [1][2][3][4][5][6][7][8][9][10] to realize the local Poincaré, de Sitter (dS) or Anti-de Sitter (AdS) symmetry. It is shown that the torsion effect in the Einstein-Cartan (EC) theory, which is the simplest model of the gauge theory of gravity, may avert the initial singularity of the homogeneous but anisotropic universe [11], where the matter fields are described by a spin fluid [12].…”

Section: Introductionmentioning

confidence: 99%

R+S2 theories of gravity without big-bang singularity

2015

Annals of Physics

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The R + S 2 theories of gravity, where S 2 denotes the quadratic torsion terms, are analyzed under three cases. In the first two cases, the matter fields are described by two different spin fluids which are not homogeneous and isotropic. In the third case, a homogeneous and isotropic torsion field is used. It is found that under all the three cases, the R+S 2 theories may avert the big-bang singularity of the RobertsonWalker universe, with three corresponding constraints on the parameters.

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“…The CS formulation of 2+1 GR makes the theory explicitly power counting renormalizable, this is because it can be reformulated in terms of a single gauge connection, 6) where the vielbein is divided by a parameter with dimensions of length, l, in order to make the one formē a l dimensionless. The generators , J AB , span the SO(2, 2) or SO(3, 1) algebras depending if the cosmological constant is negative or positive.…”

Section: Chern-simons Theoriesmentioning

confidence: 99%

“…However, it does exist the Mac Dowell-Mansouri [4] and Chamseddine-West [5] proposal (with the subsequent Stelle-West improvement [6]) to construct a gauge theory for (super) gravity a la Yang-Mills (in the sense that one of the relevant objects in the construction is a Lie algebra valued connection). This construction is elegant, somewhat reminiscent of having a topological origin and have received some considerations through the years (see for instance [7,8]).…”

Section: Introductionmentioning

confidence: 99%