2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/196511We develop a framework to study the phase space of a system consisting of a scalar field rolling down an arbitrary potential with varying slope and a background fluid, in a cosmological setting. We give analytical approximate solutions of the field evolution and discuss applications of its features to the issues of quintessence, moduli stabilisation and quintessential inflation.9 pages, 7 figures. Accepted for publication in PRDAstrophysicsGeneral Relativity and Quantum CosmologyHigh Energy Physics - PhenomenologyHigh Energy Physics - Theorytext