Topics in Beyond the Standard Model Physics

Standard Model and General relativity are two pillars of modern physics, and their reconciliation would bring a long-sought harmony in physics along with insights into the secrets of the universe. It is then natural to try and modify these theories by searching for the fundamental symmetry describing our world. In this work, I work on the implication of breaking of Lorentz symmetry and the existence of topological objects called solitons. In chapter 3, I show how a cosmologically generated Lorentz- Violating model has instability issues. I then show how the quantum corrections on Lorentz-Violating models can produce ambiguity in β-function even in first order and how these calculations can be done in both scalar QED and non-Abelian extension. In the last chapter, I demostrate how topological objects can give rise to creation and destruction of half-fermions and half-antifermions.