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Global dynamics of cosmological scalar fields -- Part I

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 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.

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Andrzej J. Maciejewski, Maria Przybylska, Tomasz Stachowiak, Marek Szydlowski. 2006-12-15. Global dynamics of cosmological scalar fields -- Part I. https://arxiv.org/abs/gr-qc/0612087

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