2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/203129We 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.This is a conflated version of arXiv:gr-qc/0612087 and arXiv:gr-qc/0703031 with a new theory sectionMathematical PhysicsGeneral Relativity and Quantum CosmologyExactly Solvable and Integrable Systems37J30, 70H06, 70H07text