Global integrability of cosmological scalar fields

Details Global integrability of cosmological scalar fields Global integrability of cosmological scalar fields

2008-03-15

arxiv.org/abs/0803.2318v2

J.Phys.A41:465101,2008

Physics

Mathematical Physics

This is a conflated version of arXiv:gr-qc/0612087 and arXiv:gr-qc/0703031 with a new theory section

Scientific paper

10.1088/1751-8113/41/46/465101

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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