Global dynamics of cosmological scalar fields -- Part I

TL;DR

This paper analyzes the integrability of cosmological scalar field models using differential Galois theory, revealing generic non-integrability and exploring connections to chaos, with focus on minimally and conformally coupled fields.

Contribution

It applies differential Galois group methods to determine integrability of scalar field cosmologies, highlighting generic non-integrability and parameter-dependent cases.

Findings

Most models are non-integrable.

Some parameter values leave integrability undecided.

Links between non-integrability and chaos are discussed.

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.