Numerical Techniques in Loop Quantum Cosmology
In this article, we review the use of numerical techniques to obtain solutions for the quantum Hamiltonian constraint in loop quantum cosmology (LQC). First, we summarize the basic features of LQC, and describe features of the constraint equations to solve - generically, these are difference (rather...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2012 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2012
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/148360 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Numerical Techniques in Loop Quantum Cosmology / D. Brizuela, D. Cartin, G. Khanna // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 75 назв. — англ. |
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Brizuela, D. Cartin, D. Khanna, G. 2019-02-18T10:53:59Z 2019-02-18T10:53:59Z 2012 Numerical Techniques in Loop Quantum Cosmology / D. Brizuela, D. Cartin, G. Khanna // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 75 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 83C45; 83Fxx; 83-08 DOI: http://dx.doi.org/10.3842/SIGMA.2012.001 https://nasplib.isofts.kiev.ua/handle/123456789/148360 In this article, we review the use of numerical techniques to obtain solutions for the quantum Hamiltonian constraint in loop quantum cosmology (LQC). First, we summarize the basic features of LQC, and describe features of the constraint equations to solve - generically, these are difference (rather than differential) equations. Important issues such as differing quantization methods, stability of the solutions, the semi-classical limit, and the relevance of lattice refinement in the difference equations are discussed. Finally, the cosmological models already considered in the literature are listed, along with typical features in these models and open issues. This paper is a contribution to the Special Issue “Loop Quantum Gravity and Cosmology”. The full collection is available at http://www.emis.de/journals/SIGMA/LQGC.html. We would like to thank M. Mart´ın-Benito for comments on the manuscript. DB acknowledges financial support from Spanish Ministry of Education through National Program No. I-D+i2008-2011. This work has been supported by the Spanish MICINN Project No. FIS2008-06078-C03-03, and by Institute of Gravitation and the Cosmos (PSU). GK acknowledges research support from NSF Grant Nos. PHY-0831631, PHY-0902026, PHY-1016906 and PHY-1135664. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Numerical Techniques in Loop Quantum Cosmology Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Numerical Techniques in Loop Quantum Cosmology |
| spellingShingle |
Numerical Techniques in Loop Quantum Cosmology Brizuela, D. Cartin, D. Khanna, G. |
| title_short |
Numerical Techniques in Loop Quantum Cosmology |
| title_full |
Numerical Techniques in Loop Quantum Cosmology |
| title_fullStr |
Numerical Techniques in Loop Quantum Cosmology |
| title_full_unstemmed |
Numerical Techniques in Loop Quantum Cosmology |
| title_sort |
numerical techniques in loop quantum cosmology |
| author |
Brizuela, D. Cartin, D. Khanna, G. |
| author_facet |
Brizuela, D. Cartin, D. Khanna, G. |
| publishDate |
2012 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
In this article, we review the use of numerical techniques to obtain solutions for the quantum Hamiltonian constraint in loop quantum cosmology (LQC). First, we summarize the basic features of LQC, and describe features of the constraint equations to solve - generically, these are difference (rather than differential) equations. Important issues such as differing quantization methods, stability of the solutions, the semi-classical limit, and the relevance of lattice refinement in the difference equations are discussed. Finally, the cosmological models already considered in the literature are listed, along with typical features in these models and open issues.
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/148360 |
| citation_txt |
Numerical Techniques in Loop Quantum Cosmology / D. Brizuela, D. Cartin, G. Khanna // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 75 назв. — англ. |
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AT brizuelad numericaltechniquesinloopquantumcosmology AT cartind numericaltechniquesinloopquantumcosmology AT khannag numericaltechniquesinloopquantumcosmology |
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2025-11-29T10:46:59Z |
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2025-11-29T10:46:59Z |
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