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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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Інститут математики НАН України
2012
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/148360 |
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irk-123456789-1483602019-02-19T01:28:44Z Numerical Techniques in Loop Quantum Cosmology Brizuela, D. Cartin, D. Khanna, G. 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. 2012 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/148360 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Brizuela, D. Cartin, D. Khanna, G. |
| spellingShingle |
Brizuela, D. Cartin, D. Khanna, G. Numerical Techniques in Loop Quantum Cosmology Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Brizuela, D. Cartin, D. Khanna, G. |
| author_sort |
Brizuela, D. |
| title |
Numerical Techniques in Loop Quantum Cosmology |
| 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 |
| publisher |
Інститут математики НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT brizuelad numericaltechniquesinloopquantumcosmology AT cartind numericaltechniquesinloopquantumcosmology AT khannag numericaltechniquesinloopquantumcosmology |
| first_indexed |
2023-05-20T17:30:03Z |
| last_indexed |
2023-05-20T17:30:03Z |
| _version_ |
1796153445542002688 |