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 Relational dynamics
3.8 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 in phenomenological equations
4.5 Isotropy: Properties and intuitive meaning of effective densities
4.6 Isotropy: Applications of effective densities
4.7 Isotropy: Phenomenological higher curvature corrections
4.8 Isotropy: Intuitive meaning of higher power corrections
4.9 Isotropy: Applications of higher-power corrections
4.10 Anisotropies
4.11 Anisotropy: Connection variables
4.12 Anisotropy: Applications
4.13 Anisotropy: Phenomenological higher curvature
4.14 Anisotropy: Implications for inhomogeneities
4.15 Inhomogeneities
4.16 Inhomogeneous matter with isotropic quantum geometry
4.17 Inhomogeneity: Perturbations
4.18 Inhomogeneous models
4.19 Inhomogeneity: Results
4.20 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 Dynamical refinements of the discreteness scale
5.6 Semiclassical limit and correction terms
5.7 Homogeneity
5.8 Diagonalization
5.9 Homogeneity: Dynamics
5.10 Inhomogeneous models
5.11 Einstein–Rosen waves
5.12 Spherical symmetry
5.13 Loop inspired quantum cosmology
5.14 Dynamics
5.15 Dynamics: General construction
5.16 Singularities
5.17 Initial/boundary value problems
5.18 Pre-classicality and boundedness
5.19 Dynamical initial conditions
5.20 Numerical and mathematical quantum cosmology
5.21 Summary
6 Effective Theory
6.1 Solvable systems and perturbation theory
6.2 Effective constraints
6.3 Isotropic cosmology
6.4 Inhomogeneity
6.5 Applications
7 Models within the Full Theory
7.1 Symmetric states
7.2 Basic operators
7.3 Quantization before reduction
7.4 Minisuperspace approximation
7.5 Quantum geometry: from models to the full theory
8 Philosophical Ramifications
8.1 Unique theories, unique solutions
8.2 The role of time
8.3 Determinism
9 Research Lines
9.1 Conceptual issues
9.2 Mathematical development of models
9.3 Applications
9.4 Homogeneous models
9.5 Future work
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