| Journal: | Brazilian journal of physics |
| Database: | PERIÓDICA |
| System number: | 000408631 |
| ISSN: | 0103-9733 |
| Authors: | Boucher, Delphine1 Weil, Jacques-Arthur2 |
| Institutions: | 1Universite de Rennes 1, Institut de Recherche Mathematique de Rennes, Rennes, Ille-et-Vilaine. Francia 2Universite de Limoges, Institut de Recherche XLIM, Limoges, Haute-Vienne. Francia |
| Year: | 2007 |
| Season: | Jun |
| Volumen: | 37 |
| Number: | 2A |
| Pages: | 398-405 |
| Country: | Brasil |
| Language: | Inglés |
| Document type: | Artículo |
| Approach: | Analítico |
| English abstract | We study the non integrability of the Friedmann-Robertson-Walker cosmological model, in continuation of the work [5] of Coehlo, Skea and Stuchi. Using Morales-Ramis theorem ([10]) and applying a practical nonintegrability criterion deduced from it, we find that the system is not completely integrable for almost all values of the parameters λ and Λ, which was already proved by the authors of [5] applying Kovacic's algorithm. Working on a level surface H = h with h 6= 0 and h 6= − 1 4λ and using the Morales-Ramis-Simo "higher variational" theory ([11]), we prove that the hamiltonian system cannot be integrable for particular values of λ among the exceptional values and that it is completely integrable in two special cases (λ = Λ = −m 2 and λ = Λ = −m 2 3 ). We conjecture that there is no other case of complete integrability and give detailed arguments towards this |
| Disciplines: | Física y astronomía, Matemáticas |
| Keyword: | Física, Matemáticas aplicadas, Relatividad general, Cosmología, Modelo de Friedman-Robertson-Walker, Sistemas hamiltonianos, Integrabilidad |
| Keyword: | Physics and astronomy, Mathematics, Physics, Applied mathematics, General relativity, Cosmology, Friedmann-Robertson-Walker model, Hamiltonian systems, Integrability |
| Full text: | Texto completo (Ver PDF) |
