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The Universe we live in has started with a bang, a very big bang. Its evolution and global structure are controlled by gravitation and its matter and radiation content. Gravitation, curving of spacetime, formulated in minimal or extended versions, provides different layers of understanding about the Universe. Einstein's General Relativity (GR) gives a description of gravity, and there are various reasons for extending it. One such extension refers to unifying the other forces in Nature with gravity in the framework of GR. The very first approach in this direction was due to Born and Infeld who have tried to unify electromagnetism with gravity. It is a generalization of metric tensor to have both symmetric and antisymmetric parts gives rise to a merging of Maxwell's theory with Einstein's theory. In later decades, attempts have been made to unify the other forces as well. In this thesis study, we extend Born-Infeld gravity to unify gravity with non- Abelian forces in a natural way. This, which we call Born-Infeld-Riemann gravity, is accomplished by devising a gravity theory based on Riemann tensor itself and subsequently generalizing this tensor to naturally involve gauge degrees of freedom. With this method, preserving the successes of Born-Infeld gravity, we are able to combine Yang- Mills fields (W, Z bosons as well as gluons) with gravity. We perform a phenomenological test of our approach by analyzing cosmic inflation generated by non-Abelian gauge fields.