Living Reviews in Relativity

"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
Open References References
Footnotes
Figures