69 research outputs found
Global integrability of cosmological scalar fields
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.Comment: This is a conflated version of arXiv:gr-qc/0612087 and
arXiv:gr-qc/0703031 with a new theory sectio
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