Geometry of gauge theories and generalized theories of gravity

Since its publication by Einstein in 1915, General Relativity (GR) has successfully passed many observational and experimental tests, making it the best model of gravity we have today. It has been able to make theoretical predictions that agree well with the data, especially at the solar system scale (more specifically, in relatively weak gravitational fields). However, thanks to technological advances over time, observations in different regions of the universe and under extreme conditions have shown that GR may be insufficient to answer some questions within the framework of its classical definition. The fact that it cannot be quantized with a recipe similar to the quantum field theories within the Standard Model is perhaps the most important theoretical problem of GR today. Despite its great successes, as mentioned above, developments over the years have left many question marks that GR still has difficulty to answer. At this point, scientists have attacked the problems that GR is inadequate for by working on alternative gravity models. These studies are very diverse and include updating / modifying / etc. the existing structure of GR and models built on structures completely different from the mathematical infrastructure of GR. In addition, with the developing computer and digital processing power, numerical gravity studies have become an activity field in their own right. In this thesis, especially, it is aimed to understand gravity as a gauge theory and alternative gravitational models established on various non-Riemannian geometrical substructures are studied. In the context of these models, the behavior of test particles and the interaction of matter field with gravity are investigated.