2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/35391We describe the geomety of a set of scalar fields coupled to gravity. We consider the formalism of a differential Z_2-graded algebra of $2\times 2$ matrices whose elements are differential forms on space-time. The connection and the vierbeins are extended to incorporate additional scalar and vector fields. The resulting action describes two universes coupled in a non-minimal way to a set of scalar fields. This picture is slightly different from the description of general relativity in the framework of non-commutative geomety.11 pages, Latex fileGeneral Relativity and Quantum CosmologyHigh Energy Physics - Theorytext