2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/35107We briefly review the arising of an inflationary phase in the Universe evolution in order to discuss an inhomogeneous cosmological solution in presence of a real self interacting scalar field minimally coupled to gravity in the region of a slow rolling potential plateau. During the inhomogeneous de Sitter phase the scalar field dominant term is a function of the spatial coordinates only. We apply this generic solution to the Coleman-Weinberg potential and to the Lemaitre-Tolman metric. This framework specialized nearby the FLRW model allows a classical origin for the inhomogeneous perturbations spectrum.10 pages, Invited contribution for the 'New Talents' Session for the Proceedings of the 42nd International School of Subnuclear Physics, Erice, 29 Aug- 6 Sept 2004, Italy -- 'J.Bell' DiplomaGeneral Relativity and Quantum Cosmologytext