Brane-world quantum gravity (original) (raw)

Classical and quantum aspects of brane-world cosmology

AIP Conference Proceedings, 2011

We give a brief overview of several models in brane-world cosmology. In particular, we focus on the asymmetric DGP and Regge-Teiltelboim models. We present the associated equations of motion governing the dynamics of the brane and their corresponding Friedmann-like equations. In order to develop the quantum Regge-Teiltelboim type cosmology we construct its Ostrogradski Hamiltonian formalism which naturally leads to the corresponding Wheeler-DeWitt equation. In addition, we comment on possible generalizations for these models including second order derivative geometrical terms.

Quantum Mechanical Formulation Of Quantum Cosmology For Brane-World Effective Action

2003

Canonical quantization of the Brane-World effective action presented by Kanno and Soda containing higher order curvature invariant terms, has been performed. It requires introduction of an auxiliary variable. As observed in a series of publications by Sanyal and Modak, here again we infer that properly chosen auxiliary variable leads to a Schrodinger like equation where the kinetic part of a canonical variable disentangles from the rest of the variables giving a natural quantum mechanical flavour of time. Further, the effective Hamiltonian turns out to be hermitian, leading to the continuity ewuation. Thus, a quantum mechanical probability inter pretation is plausible. Finally, the extremization of the effective potential leads to Einstein's equation and a well behaved classical solution, which is a desirable feature of the gravitational action containing higher order curvature invariant terms.

Hamiltonian Theory of Brane-World Gravity

The Eleventh Marcel Grossmann Meeting, 2008

A brane-world universe consists of a 4-dimensional brane embedded into a 5-dimensional space-time (bulk). We apply the Arnowitt-Deser-Misner decomposition to the braneworld, which results in a 3+1+1 break-up of the bulk. We present the canonical theory of brane cosmology based on this decomposition. The Hamiltonian equations allow for the study of any physical phenomena in brane gravity. This method gives new prospects for studying the initial value problem, stability analysis, brane black holes, cosmological perturbation theory and canonical quantization in brane-worlds.

Classical and quantum brane cosmology

AIP Conference Proceedings, 2001

The first part of this lecture quickly touches upon some important but infrequently discussed issues in large extra dimension and warped extra dimension scenarios, with particular reference to effects in the early universe. The second part discusses a modification and extension of an earlier proposal by Brown and Teitelboim to relax the effective cosmological term by nucleation of fundamental membranes.

New views on classical and quantum Brans-Dicke theory

arXiv: General Relativity and Quantum Cosmology, 2016

The Brans-Dicke action is one of the most natural extensions of the Einstein-Hilbert action. It is based on the introduction of a fundamental scalar field that effectively incorporates a dynamics to the gravitational coupling GGG. In spite of the diverse motivations and the rich phenomenology that comes from its solutions, Solar System tests impose strong constraints on the Brans-Dicke theory, rendering it indistinguishable from General Relativity. In the present text, new perspectives for the Brans-Dicke theory are presented, based on the possibility that the scalar field presented in the BD theory can be external, as well as on the applications to black hole physics and the primordial universe.

D-brane approach to black hole quantum mechanics

Nuclear Physics B, 1996

Strominger and Vafa have used D-brane technology to identify and precisely count the degenerate quantum states responsible for the entropy of certain extremal, BPS-saturated black holes. Here we give a Type-II D-brane description of a class of extremal and nonextremal five-dimensional Reissner-Nordström solutions and identify a corresponding set of degenerate D-brane configurations. We use this information to do a string theory calculation of the entropy, radiation rate and "Hawking" temperature. The results agree perfectly with standard Hawking results for the corresponding nearly extremal Reissner-Nordström black holes. Although these calculations suffer from open-string strong coupling problems, we give some reasons to believe that they are nonetheless qualitatively reliable. In this optimistic scenario there would be no "information loss" in black hole quantum evolution.

Quantum mechanics and geodesic deviation in the brane world

2009

Abstract. We investigate the induced geodesic deviation equations in the brane world models, in which all the matter forces except gravity are confined on the 3-brane. Also, the Newtonian limit of induced geodesic deviation equation is studied. We show that in the first Randall-Sundrum model the Bohr–Sommerfeld quantization rule is as a result of consistency between the geodesic and geodesic deviation equations.

An Alternative to Matter Localization in the" Brane World": An Early Proposal and its Later Improvements

Physics Letters A 116 (1986) 1-5, 1986

We formulate a first order action principle in a higher dimensional space M_N in which we embed spacetime. The action I is essentially an “area” of a four-dimensional spacetime V_4 weighted with a matter density omega\omegaomega in M_N. For a suitably chosen omega\omegaomega we obtain on V_4 a set of worldlines. It is shown that these worldlines are geodesics of V_4, provided that V_4 is a solution to our variational procedure. Then it follows that our spacetime satisfies the Einstein equations for dust – apart from an additional term with zero covariant divergence. (This extra term was shown in a previous paper to be exactly zero at least in the case of the cosmological dust model.) Thus we establish a remarkable connection of the extrinsic spacetime theory with the intrinsic general relativity. This step appears to be important for quantum gravity.

Hints of a new relativity principle from p-brane quantum mechanics

Chaos Solitons & Fractals, 2000

This report is an extension of previous one hep-th/9812189. Several quantum mechanical wave equations for p-branes are proposed. The most relevant p-brane quantum mechanical wave equations determine the quantum dynamics involving the creation/destruction of p-dimensional loops of topology S p , moving in a D dimensional spacetime background, in the quantum state Φ. To implement full covariance we are forced to enlarge the ordinary Relativity principle to a new Relativity principle, suggested earlier by the author based on the construction of C-space, and also by Pezzaglia's Polydimensional Relativity, where all dimensions and signatures of spacetime should be included on the same footing.

(Non)-singular brane-world cosmology induced by quantum effects in five-dimensional dilatonic gravity

Physical Review D, 2000

5d dilatonic gravity (bosonic sector of gauged supergravity) with nontrivial bulk potential and with surface terms (boundary cosmological constant and trace anomaly induced effective action for brane quantum matter) is considered. For constant bulk potential and maximally SUSY Yang-Mills theory (CFT living on the brane) the inflationary brane-world is constructed. The bulk is singular asymptotically AdS space with non-constant dilaton and dilatonic de Sitter or hyperbolic brane is induced by quantum matter effects. At the same time, dilaton on the brane is determined dynamically. This all is natural realization of warped compactification in AdS/CFT correspondence. For fine-tuned toy example of non-constant bulk potential we found the nonsingular dilatonic brane-world where bulk again represents asymptotically AdS space and de Sitter brane (inflationary phase of observable Universe) is induced exclusively by quantum effects. The radius of the brane and dilaton are determined dynamically. The analytically solvable example of exponential bulk potential leading to singular asymptotically AdS dilatonic bulk space with de Sitter (or hyperbolic) brane is also presented. In all cases under discussion the gravity on the brane is trapped via Randall-Sundrum scenario. It is shown that qualitatively the same types of brane-worlds occur when quantum brane matter is described by N dilaton coupled spinors.