Bimetric Models of Gravity and Cosmology in the Early Universe

In this dissertation, we explore models based on the idea that there are two metrics in spacetime: One describes the standard gravity, and the other provides a geometry in which matter fields propagate. In order to do that, we provide the essentials of Finsler geometry and the rules to induce a metric for the propagation of matter. Such a description will cover some of the most critical features related to the field necessary to do the induction, these will arise in an attempt to build an action for this field. And finally, we provide an example to study the homogeneous limit of background FLRW equations for the cosmological model and the role of Lorentz symmetry breaking to provide a graceful exit.