2006/12/13 by Andrzej J. Maciejewski, Maria Przybylska, Maciejewski, Andrzej J. +5 · 1 citation
Mathematics · Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #gr-qc #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.gr-qc/0612087
14 pages, added acknowledgements
arxiv created 2006/12/15 · arxiv updated 2009/12/01
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 are non-integrable, although there still exist some values of parameters for which integrability remains undecided. We also draw a connection with chaos present in such cosmological models. The first part of the article deals with minimally coupled fields, and the second treats the conformal couping.