Global integrability of cosmological scalar fields
Mathematical Physics
2008-11-26 v2 General Relativity and Quantum Cosmology
math.MP
Exactly Solvable and Integrable Systems
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.
Cite
@article{arxiv.0803.2318,
title = {Global integrability of cosmological scalar fields},
author = {Andrzej J. Maciejewski and Maria Przybylska and Tomasz Stachowiak and Marek Szydlowski},
journal= {arXiv preprint arXiv:0803.2318},
year = {2008}
}
Comments
This is a conflated version of arXiv:gr-qc/0612087 and arXiv:gr-qc/0703031 with a new theory section