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Article Dans Une Revue Brazilian Journal of Physics Année : 2007

About the non-integrability in the Friedmann-Robertson-Walker cosmological model

Jacques-Arthur Weil
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Résumé

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 X and A, which was already proved by the authors of [5] applying Kovacic's algorithm. Working on a level surface H = h with h not equal 0 and h not equal -1/4 lambda and using the Morales-Ramis-Simo "higher variational" theory ([11]), we prove that the hamiltonian system cannot be integrable for particular values of lambda among the exceptional values and that it is completely integrable in two special cases (lambda =Lambda =-m(2) and lambda = Lambda=-m(2)/3). We conjecture that there is no other case of complete integrability and give detailed arguments towards this.
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Dates et versions

hal-00364562 , version 1 (26-02-2009)

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  • HAL Id : hal-00364562 , version 1

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Delphine Boucher, Jacques-Arthur Weil. About the non-integrability in the Friedmann-Robertson-Walker cosmological model. Brazilian Journal of Physics, 2007, 37 (2A), pp.398-405. ⟨hal-00364562⟩
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