Vol. 11 (2008) > lrr-2008-4

doi: 10.12942/lrr-2008-4
Living Rev. Relativity 11 (2008), 4

Loop Quantum Cosmology

1 Institute for Gravitational Physics and Geometry, The Pennsylvania State University, University Park, PA 16802, U.S.A.

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Article Abstract

Quantum gravity is expected to be necessary in order to understand situations in which classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e., the fact that the backward evolution of a classical spacetime inevitably comes to an end after a finite amount of proper time. This presents a breakdown of the classical picture and requires an extended theory for a meaningful description. Since small length scales and high curvatures are involved, quantum effects must play a role. Not only the singularity itself but also the surrounding spacetime is then modified. One particular theory is loop quantum cosmology, an application of loop quantum gravity to homogeneous systems, which removes classical singularities. Its implications can be studied at different levels. The main effects are introduced into effective classical equations, which allow one to avoid the interpretational problems of quantum theory. They give rise to new kinds of early-universe phenomenology with applications to inflation and cyclic models. To resolve classical singularities and to understand the structure of geometry around them, the quantum description is necessary. Classical evolution is then replaced by a difference equation for a wave function, which allows an extension of quantum spacetime beyond classical singularities. One main question is how these homogeneous scenarios are related to full loop quantum gravity, which can be dealt with at the level of distributional symmetric states. Finally, the new structure of spacetime arising in loop quantum gravity and its application to cosmology sheds light on more general issues, such as the nature of time.

Keywords: Ashtekar variables, Big Bang, canonical quantum gravity, cosmology, effective equations, equations of motion, inflation, quantum cosmology, singularities, symmetry, time, difference equations

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Article Citation

Since a Living Reviews in Relativity article may evolve over time, please cite the access <date>, which uniquely identifies the version of the article you are referring to:

Martin Bojowald,
"Loop Quantum Cosmology",
Living Rev. Relativity 11,  (2008),  4. URL (cited on <date>):
http://www.livingreviews.org/lrr-2008-4

Article History

ORIGINAL http://www.livingreviews.org/lrr-2005-11
Title Loop Quantum Cosmology
Author Martin Bojowald
Date accepted 28 October 2005, published 8 December 2005
UPDATE http://www.livingreviews.org/lrr-2008-4
Title Loop Quantum Cosmology
Author Martin Bojowald
Date accepted 26 May 2008, published 2 July 2008
Changes Updated and added 108 new references.

New:

Sect. 3.7 on relational dynamics
Sect. 4.7 on phenomenological higher curvature corrections
Sect. 4.8 on their intuitive meaning
Sect. 4.9 on applications
Sect. 4.13 on phenomenological higher curvature in anisotropic models
Sect. 4.14 bottom paragraph on the BKL picture
Sect. 4.19.1 paragraph
Sect. 4.19.5 on cosmological perturbation theory
Sect. 4.19.6 on equations of state
Sect. 4.19.7 on big bang nucleosynthesis
Sect. 4.20 extended summary
Sect. 5.5 on dynamical refinements of the discreteness scale
Sect. 5.20 on numerical and mathematical quantum cosmology
Sect. 6 on effective theory
Sect. 7.1 two bottom paragraphs on symmetric states
Sect. 9 some updates according to recent progress

Systematic changes:

Sect. 4: consider different types of quantum corrections from loop
quantum gravity: inverse volume and holonomies. Emphasize quantum
back-reaction with reference to new Sect. 6

Sect. 4.17: several changes on inhomogeneous perturbations

Sect. 5.4: several remarks added on possible scale dependence of the
discreteness in Hamiltonian constraint operators as well as new
constructions of operators for closed and open models

Sect. 5.6.2: update of procedure to derive effective equations, with
reference to new Sect. 6

Corrections in Sect. 5.11 on Einstein-Rosen waves
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