New Approaches to the Hierarchy Problem and their Signatures from Microscopic to Cosmic Scales
It's an exciting time in particle theory. Fantastic experimental effort has revealed that the major ideas of the past few decades of particle theory are increasingly in tension with empirical data---underscoring the need for new ideas and strategies. In this thesis we focus on the application of this philosophy toward the hierarchy problem. We begin with a pedagogical introduction aimed at grounding the hierarchy problem with a clear understanding of renormalization and a comprehensive discussion of the problem while debunking common confusions. We survey classic approaches and argue that the LHC data has qualitatively changed the problem. We discuss the Twin Higgs as the avatar of the `neutral naturalness' strategy, and its exotic signatures which shift the signals of naturalness away from the energy frontier. Finally, we suggest a new trail for the naturalness paradigm: violations of effective field theory---as demanded by quantum gravity---challenge the assumptions of the space of solutions and suggest qualitatively new avenues of pursuit.