Quantum geometrodynamics of the Bianchi IX cosmological model

@article{Kheyfets2006QuantumGO,
  title={Quantum geometrodynamics of the Bianchi IX cosmological model},
  author={Arkady Kheyfets and Warner A. Miller and Ruslan Vaulin},
  journal={Classical and Quantum Gravity},
  year={2006},
  volume={23},
  pages={4333-4351}
}
The canonical quantum theory of gravity?quantum geometrodynamics (QG)?is applied to the homogeneous Bianchi type IX cosmological model. As a result, a framework for the quantum theory of homogeneous cosmologies is developed. We show that the theory is internally consistent and prove that it possesses the correct classical limit (the theory of general relativity). To emphasize the special role that the constraints play in this new theory, we compare it to the traditional ADM square-root and… 
6 Citations
Inhomogeneous quantum Mixmaster: from classical towards quantum mechanics
Starting from the Hamiltonian formulation for the inhomogeneous Mixmaster dynamics, we approach its quantum features through the link of the quasi-classical limit. We fix the proper operator-ordering
CLASSICAL AND QUANTUM FEATURES OF THE MIXMASTER SINGULARITY
This review paper is devoted to analyzing the main properties of the cosmological singularity associated with the homogeneous and inhomogeneous Mixmaster model. After the introduction of the main
On the Dynamics of Bianchi IX Cosmological Models
A cosmological description of the universe is proposed in the context of Hamiltonian formulation of a Bianchi IX cosmology minimally coupled to a massless scalar field. The classical and quantum
Some examples for different descriptions of energy–momentum density in the context of Bianchi IX cosmological model
Based on the Bianchi type IX metric, we calculate the energy and momentum density components of the gravitational field for the five different definitions of energy–momentum, namely, Tolman,
Quantum Kasner transition in a locally rotationally symmetric Bianchi II universe
The Belinski-Khalatnikov-Lifshitz (BKL) conjecture predicts a chaotic alternation of Kasner epochs in the evolution of generic classical spacetimes towards a spacelike singularity. As a first step

References

SHOWING 1-10 OF 27 REFERENCES
Quantum Theory of Gravity. I. The Canonical Theory
Following an historical introduction, the conventional canonical formulation of general relativity theory is presented. The canonical Lagrangian is expressed in terms of the extrinsic and intrinsic
Constraints in Quantum Geometrodynamics
We compare different treatments of the constraints in canonical quantum gravity. The standard approach on the superspace of 3-geometries treats the constraints as the sole carriers of the dynamic
Quantum geometrodynamics: Quantum-driven many-fingered time.
TLDR
This work presents a new approach to the quantization of gravity wherein the concept of time is derived by imposing the constraints as expectation-value equations over the true dynamical degrees of freedom of the gravitational field---a representation of the underlying anisotropy of space.
The Issue of Time Evolution in Quantum Gravity
We discuss the relation between the concept of time and the dynamic structure of quantum gravity. We briefly review the problems of time associated with the standard procedures of gravity
Generalized quantum theory of recollapsing homogeneous cosmologies
A sum-over-histories generalized quantum theory is developed for homogeneous minisuperspace type A Bianchi cosmological models, focussing on the particular example of the classically recollapsing
TIME IN QUANTUM GEOMETRODYNAMICS
We revisit the issue of time in quantum geometrodynamics and suggest a quantization procedure on the space of true dynamic variables. This procedure separates the issue of quantization from enforcing
Homogeneous Relativistic Cosmologies
Addressing a variety of theoretical cosmological problems, and emphasizing a mathematical approach, this volume nicely complements Peebles' "Physical Cosmology" (Princeton Series in Physics, 1971).
Canonical Quantum Gravity
This is a review of the aspirations and disappointments of the canonical quantization of geometry. I compare the two chief ways of looking at canonical gravity, geometrodynamics and connection
What is Quantum Theory of Gravity
We present a line by line derivation of canonical quantum mechanics stemming from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of
Quantum Cosmology
IN cosmology a continuous fluid is used to represent the complex contents of the universe. Homogeneous and isotropic models then show that the universe originated from a space–time singularity of
...
1
2
3
...