Abstract

Quantum gravity is expected to be necessary in order to understand situations where 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 space-time 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 space-time is then modified. One particular realization 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. Main effects are introduced into effective classical equations which allow to avoid 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 to extend space-time 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 space-time arising in loop quantum gravity and its application to cosmology sheds new light on more general issues such as time.

Original languageEnglish (US)
Pages (from-to)1-99
Number of pages99
JournalElectronic Journal of Combinatorics
Volume12
Issue number1 R
StatePublished - Dec 8 2005

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Cosmology
Quantum Cosmology
Quantum Gravity
Gravitation
Singularity
Space-time
Breakdown
Relativity
Quantum theory
Difference equations
Wave functions
Early Universe
Necessary
Quantum Effects
Main Effect
Phenomenology
Quantum Theory
General Relativity
Length Scale
Wave Function

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics

Cite this

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Loop quantum cosmology. / Bojowald, Martin.

In: Electronic Journal of Combinatorics, Vol. 12, No. 1 R, 08.12.2005, p. 1-99.

Research output: Contribution to journalReview article

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