Brane classical and quantum cosmology from an effective action
arXiv:gr-qc/0303115 · doi:10.1103/PhysRevD.68.066009
Abstract
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 Friedmann-Lemaitre-Robertson-Walker (FLRW) model. The effective action governing the model in the mini-superspace 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.
Shortened to match version accepted by Phys. Rev. D (unabridged text found in version 2), 42 pages, 9 figures, Rextex4
References in corpus (41)
- A Large Mass Hierarchy from a Small Extra Dimension
- An Alternative to Compactification
- The Hierarchy Problem and New Dimensions at a Millimeter
- New Dimensions at a Millimeter to a Fermi and Superstrings at a TeV
- Phenomenology, Astrophysics and Cosmology of Theories with Sub-Millimeter Dimensions and TeV Scale Quantum Gravity
- Eleven-Dimensional Supergravity on a Manifold with Boundary
- Kaluza-Klein Gravity
- An exotic class of Kaluza-Klein models
- Dynamics of Anti-de Sitter Domain Walls
- Spacetime as a membrane in higher dimensions
- Gravitational Leakage into Extra Dimensions: Probing Dark Energy Using Local Gravity
- Brane World Inflation Induced by Quantum Effects
- Cosmological production of charged black hole pairs
- Quantum cosmological perfect fluid models
- Friedmann-Robertson-Walker brane cosmological equations from the five-dimensional bulk (A)dS black hole
- Quantum (in)stability of dilatonic AdS backgrounds and holographic renormalization group with gravity
- The Causal Interpretation of Dust and Radiation Fluids Non-Singular Quantum Cosmologies
- CFT and Entropy on the Brane
- Quantum Cosmology and AdS/CFT
- Living on the edge: cosmology on the boundary of anti-de Sitter space
- Bulk effects in the cosmological dynamics of brane-world scenarios
- Charged Topological Black Hole Pair Creation
- Radiation-Dominated Quantum Friedmann Models
- Geodetic Brane Gravity
- Bouncing and cyclic universes from brane models
- Pair Creation of Black Holes by Domain Walls
- Braneworld Instantons
- Dynamical Vacuum in Quantum Cosmology
- Exact braneworld cosmology induced from bulk black holes
- Reduced phase space formalism for spherically symmetric geometry with a massive dust shell
- Self-Adjoint Wheeler-DeWitt Operators, the Problem of Time and the Wave Function of the Universe
- AdS/CFT and quantum-corrected brane entropy
- Birth of the Brane World
- Stealth Branes
- Gauge Invariant Hamiltonian Formalism for Spherically Symmetric Gravitating Shells
- Tunneling into the Randall-Sundrum Brane World
- Does brane cosmology have realistic principles?
- Bouncing and cyclic universes in the charged AdS bulk background
- Quantum Collapse of a Small Dust Shell
- Semiclassical instability of the brane-world: Randall-Sundrum bubbles
- Classical analogous of quantum cosmological perfect fluid models