"Loop Quantum Cosmology"
by
Martin Bojowald
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Abstract
1
Introduction
2
The Viewpoint of Loop Quantum Cosmology
3
Loop Quantum Gravity
3.1
Geometry
3.2
Ashtekar variables
3.3
Representation
3.4
Function spaces
3.5
Composite operators
3.6
Hamiltonian constraint
3.7
Open issues
4
Loop Cosmology
4.1
Isotropy
4.2
Isotropy: Connection variables
4.3
Isotropy: Implications of a loop quantization
4.4
Isotropy: Effective densities and equations
4.5
Isotropy: Properties and intuitive meaning
4.6
Isotropy: Applications
4.7
Anisotropies
4.8
Anisotropy: Connection variables
4.9
Anisotropy: Applications
4.10
Anisotropy: Implications for inhomogeneities
4.11
Inhomogeneities
4.12
Inhomogeneous matter with isotropic quantum geometry
4.13
Inhomogeneity: Perturbations
4.14
Inhomogeneous models
4.15
Inhomogeneity: Results
4.16
Summary
5
Loop quantization of symmetric models
5.1
Symmetries and backgrounds
5.2
Isotropy
5.3
Isotropy: Matter Hamiltonian
5.4
Isotropy: Hamiltonian constraint
5.5
Semiclassical limit and correction terms
5.6
Homogeneity
5.7
Diagonalization
5.8
Homogeneity: Dynamics
5.9
Inhomogeneous models
5.10
Einstein-Rosen waves
5.11
Spherical symmetry
5.12
Loop inspired quantum cosmology
5.13
Dynamics
5.14
Dynamics: General construction
5.15
Singularities
5.16
Initial/boundary value problems
5.17
Pre-classicality and boundedness
5.18
Dynamical initial conditions
5.19
Summary
6
Models within the Full Theory
6.1
Symmetric states
6.2
Basic operators
6.3
Quantization before reduction
6.4
Minisuperspace approximation
6.5
Quantum geometry from models to the full theory
7
Philosophical Ramifications
7.1
Unique theories, unique solutions
7.2
The role of time
7.3
Determinism
8
Research Lines
8.1
Conceptual issues
8.2
Mathematical development of models
8.3
Applications
8.4
Homogeneous models
8.5
Outlook
A
Invariant connections
A.1
Partial backgrounds
A.2
Classification of symmetric principal fiber bundles
A.3
Classification of invariant connections
B
Examples
B.1
Homogeneous models
B.2
Isotropic models
B.3
Spherical symmetry
References
Footnotes
Figures