2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/198201The nonminimal coupling (NMC) of the scalar field to the Ricci curvature is unavoidable in many cosmological scenarios. Inflation and quintessence models based on nonminimally coupled scalar fields are studied, with particular attention to the balance between the scalar potential and the NMC term in the action. NMC makes acceleration of the universe harder to achieve for the usual potentials, but it is beneficial in obtaining cosmic acceleration with unusual potentials. The slow-roll approximation with NMC, conformal transformation techniques, and other aspects of the physics of NMC are clarified.36 pages, LaTeX. Typos in Eq. (2.5) correctedGeneral Relativity and Quantum CosmologyAstrophysicsHigh Energy Physics - Theorytext