Geodetic brane gravity

Karasik, David; Davidson, Aharon

doi:10.1103/physrevd.67.064012

Cited by 82 publications

(155 citation statements)

References 33 publications

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“…Also represented in the scheme are Dirac's extensible model (D), and the Dvali-Gabadadze-Porrati (DGP) and Collins-Holdom (CH) extensions of the RS model. the past, but given its built-in Einstein limit and a handful of attractive features [13,14] (in particular, a dark companion [13] to any energy density, a quadratic Hamiltonian formalism [15], and a rather novel approach to brane nucleation [16]), it offers a unique deviation from General Relativity. The associated so-called Geodesic Brane Gravity (GBG) is conveniently parametrized by a conserved 'bulk energy' (see ω in Fig.1) which fades away at the Einstein limit.…”

Section: Figmentioning

confidence: 99%

Dirac relaxation of the Israel junction conditions: Unified Randall-Sundrum brane theory

Davidson

Gurwich

2006

Phys. Rev. D

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Following Dirac's brane variation prescription, the brane must not be deformed during the variation process, or else the linearity of the variation may be lost. Alternatively, the variation of the brane is done, in a special Dirac frame, by varying the bulk coordinate system itself. Imposing appropriate Dirac style boundary conditions on the constrained 'sandwiched' gravitational action, we show how Israel junction conditions get relaxed, but remarkably, all solutions of the original Israel equations are still respected. The Israel junction conditions are traded, in the Z2-symmetric case, for a generalized Regge-Teitelboim type equation (plus a local conservation law), and in the generic Z2-asymmetric case, for a pair of coupled Regge-Teitelboim equations. The Randall-Sundrum model and its derivatives, such as the Dvali-Gabadadze-Porrati and the Collins-Holdom models, get generalized accordingly. Furthermore, Randall-Sundrum and Regge-Teitelboim brane theories appear now to be two different faces of the one and the same unified brane theory. Within the framework of unified brane cosmology, we examine the dark matter/energy interpretation of the effective energy/momentum deviations from General Relativity. I. INTRODUCTIONIn an almost forgotten paper [1] entitled "An extensible model of the electron", Dirac has made an attempt to picture a classical spinless electron as a breathing bubble in the electromagnetic field 'with no constraints fixing its size and shape'. Some positive surface tension has been invoked in order 'to prevent the electron from flying apart under the Coulomb repulsion of it surface charge'. On the practical side, this naive model has not made any impact on particle physics, so in this paper, we make no use of the model itself. On the field theoretical side, however, although gravity was switched off in this paper, it was nonetheless the first brane model. The equations of motion are derivable from an action principle, and in particular, the model offers a detailed prescription how to consistently perform brane variation. In the present paper, we switch on gravity, and apply the Dirac brane variation prescription to modern brane theories.Our main result is that the Israel[2] junction conditions (IJC), which are known to play a central role in all modern brane theories, get in fact relaxed. While every IJC solution is still strictly respected, it represents now a whole (continuous) family of new solutions. This opens the door for brane unification. To be more specific, as schematically illustrated in Fig.1 The Randall-Sundrum theory is very well known, and has rightly attracted lots of attention from General Relativity [7], cosmology [8] in particular, and also from string theory[9] points of view. See Ref.[10] for some brane world reviews, and Ref.[11] for some earlier brane models. The much older Regge-Teitelboim theory, on the other hand, a generalized Nambu-Goto type brane theory [3] for quantum gravity, has remained quite unfamiliar. This is partially due to the fact that the theory was o...

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Section: Figmentioning

confidence: 99%

Dirac relaxation of the Israel junction conditions: Unified Randall-Sundrum brane theory

Davidson

Gurwich

2006

Phys. Rev. D

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“…The case where there is some conformal field theory living on the brane has also been considered for various bulk manifolds [42,43,44]. Related to these studies are works that consider the quantum creation (or decay) of brane universes via saddle-point approximations to path integrals [45,46,47] -often in bulk manifolds other than S-AdS 5 -as well as papers that consider the classical and quantum dynamics of "geodetic brane universes" [48,49,50].…”

Section: Introductionmentioning

confidence: 99%

Brane classical and quantum cosmology from an effective action

2003

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Motivated by the Randall-Sundrum brane-world scenario, we discuss the classical and quantum dynamics of a (d + 1)-dimensional boundary wall between a pair of (d + 2)-dimensional topological Schwarzschild-AdS black holes. We assume there are quite general -but not completely arbitrary -matter fields living on the boundary "brane universe" and its geometry is that of an FriedmannLemaître-Robertson-Walker (FLRW) model. The effective action governing the model in the minisuperspace approximation is derived. We find that the presence of black hole horizons in the bulk gives rise to a complex action for certain classically allowed brane configurations, but that the imaginary contribution plays no role in the equations of motion. Classical and instanton brane trajectories are examined in general and for special cases, and we find a subset of configuration space that is not allowed at the classical or semi-classical level; these correspond to spacelike branes carrying tachyonic matter. The Hamiltonization and Dirac quantization of the model is then performed for the general case; the latter involves the manipulation of the Hamiltonian constraint before it is transformed into an operator that annihilates physical state vectors. The ensuing covariant Wheeler-DeWitt equation is examined at the semi-classical level, and we consider the possible localization of the brane universe's wavefunction away from the cosmological singularity. This is easier to achieve for branes with low density and/or spherical spatial sections.

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“…In the RT model second derivatives of the fields appear in the action, and like general relativity these higher derivative terms may be clubbed in a surface term. In the usual formulation this surface term is dropped [3], thereby reducing the original model to a first-order theory. However, this makes the Hamiltonian formulation of the model problematic [3].…”

Section: Introductionmentioning

confidence: 99%

“…In the usual formulation this surface term is dropped [3], thereby reducing the original model to a first-order theory. However, this makes the Hamiltonian formulation of the model problematic [3]. These problems are bypassed by introducing an auxiliary field [3].…”

Section: Introductionmentioning

confidence: 99%

New Hamiltonian analysis of Regge-Teitelboim minisuperspace cosmology

Banerjee

Mukherjee²,

Paul

2014

Phys. Rev. D

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A new Hamiltonian formulation of the minisuperspace cosmology following from the geodetic brane gravity model introduced by Regge and Teitelboim is presented. The model is considered in the framework of higher derivative theories which facilitates Hamiltonian formulation. The analysis is done using the equivalent first-order approach. The gauge generator containing the exact number of gauge parameters is constructed. Equivalence between the gauge and reparametrization symmetries has been demonstrated. Complete gauge fixed computations have been provided and formal quantization is done indicating the Wheeler DeWitt equation. Compatibility with existing results is shown.

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Geodetic brane gravity

Cited by 82 publications

References 33 publications

Dirac relaxation of the Israel junction conditions: Unified Randall-Sundrum brane theory

Dirac relaxation of the Israel junction conditions: Unified Randall-Sundrum brane theory

Brane classical and quantum cosmology from an effective action

New Hamiltonian analysis of Regge-Teitelboim minisuperspace cosmology

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