"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
References
Footnotes
Figures