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arXiv · 0803.2318

Global integrability of cosmological scalar fields

Andrzej J. Maciejewski·Maria Przybylska·Tomasz Stachowiak·Marek Szydlowski
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Abstract

We investigate the Liouvillian integrability of Hamiltonian systems describing a universe filled with a scalar field (possibly complex). The tool used is the differential Galois group approach, as introduced by Morales-Ruiz and Ramis. The main result is that the generic systems with minimal coupling are non-integrable, although there still exist some values of parameters for which integrability remains undecided; the conformally coupled systems are only integrable in four known cases. We also draw a connection with chaos present in such cosmological models, and the issues of integrability restricted to the real domain.

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Andrzej J. Maciejewski, Maria Przybylska, Tomasz Stachowiak, Marek Szydlowski. 2008-08-19. Global integrability of cosmological scalar fields. https://doi.org/10.1088/1751-8113/41/46/465101

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