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Numerical Techniques in Loop Quantum Cosmology
Репозиторій DSpace/Manakin
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- Фізико-технічні та математичні науки
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8
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- Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8, випуск за цей рік
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Numerical Techniques in Loop Quantum Cosmology
Інший ID:
2010 Mathematics Subject Classification: 83C45; 83Fxx; 83-08
DOI: http://dx.doi.org/10.3842/SIGMA.2012.001
DOI: http://dx.doi.org/10.3842/SIGMA.2012.001
Посилання:
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.
Підтримка:
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.
Дата:
2012
Переглядів:
604
Завантажень:
254
Анотація:
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.
