Anabalón Dupuy, AndrésMedina Medina, Perla Soledad2024-11-212024-11-212024https://repositorio.udec.cl/handle/11594/9886Tesis presentada para optar al grado de Doctor en Ciencias FísicasThis thesis addresses two fundamental topics in the field of gravity. First, a reformulation of the Mimetic theory of gravity in first-order formalism for differential forms, i.e., the mimetic version of Einstein-Cartan-Kibble-Sciama (ECKS) gravity. Here we consider different possibilities on how torsion is af- fected by conformal transformations and discuss how this translates into the interpolation between two different conformal transformations of the spin con- nection, parameterized with a zero-form parameter λ. We prove that regardless of the type of transformation one chooses, in this setting torsion remains as a non-propagating field. We also discuss the conservation of the mimetic stress- energy tensor and show that the trace of the total stress-energy tensor is not null but depends on both, the value of λ and spacetime torsion. Second, the Einstein-Hilbert action is studied in the first-order formalism, considering the coupling of a scalar field to different topological invariants. The implications of this coupling on the dynamics of the gravitational field and the evolution of the early universe are analyzed. The results obtained contribute to a better understanding of gravity and its relationship with the topology of spacetime. Second, the Einstein-Hilbert action is studied in the first-order formalism, con- sidering the coupling of a scalar field to different topological invariants. The implications of these couplings on the field equations are analyzed. The re- sults obtained shed light on a theoretical framework where it could be easier to introduce couplings of scalar fields to the geometry.enCC BY-NC-ND 4.0 DEED Attribution-NonCommercial-NoDerivs 4.0 InternationalTorsión⁠Topología de variedades en dimensión cuatro⁠Campos gravitacionalesThesis