2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/231380The acceleration of the universe is described as a dynamical effect of the extrinsic curvature of space-time. By extending previous results, the extrinsic curvature is regarded as an independent spin-2 field, determined by a set of non-linear equations similar to Einstein's equations. In this framework, we investigate some cosmological consequences of this class of scenarios and test its observational viability by performing a statistical analysis with current type Ia Supernova data.10 pages, 3 figures, LaTeXCosmology and Nongalactic Astrophysicstext