Model Building and Phenomenology in Grand Unified Theories

The Standard Model (SM) of particle physics is known to suffer from several flaws, and the upcoming generation of experiments may shed some light onto their solution. Whether there is evidence of new physics or not, theories Beyond the SM (BSM) must be able to accommodate and explain the coming data. The lack of signs of BSM physics so far, calls for a exhaustive exploration beyond the minimal models, in particular Grand Unified theories, for they are able to solve some of the issues of the SM and can make testable predictions. Therefore, we attempt to develop a framework to build Grand Unified models, capable of generating and analysing general non-minimal models. In order to do so, first we create a computational tool to handle the group theoretical component, calculating properties of Lie Groups and their representations. Among them, those of interest to the model building process are the calculation of breaking chains from a group to a subgroup, the decomposition of representations of a group into those of a subgroup and the construction of group invariants. Using some of the capabilities of the group tool, and starting with a set of representations and a breaking chain, we generate all the conceivable models, classifying them to satisfy conditions such as anomaly cancellation and symmetry breaking. We then move on to study the unification of gauge couplings on the models and its consequences on the scale of unification and the scale of supersymmetry breaking, to later constrain them to match phenomenological observables, such as proton decay or current collider searches. We conclude by focusing the analysis on two specific models, a minimal supersymmetric SO(10) model, with some interesting predictions for future colliders, and a flipped SU(5)xU(1) model, which serves as the triggering mechanism for the end of the inflationary epoch in the early universe