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Open questions related to the mechanism of electroweak symmetry breaking, the phenomenology and nature of the recently discovered Higgs boson, and the identity of dark matter are leading motivations for the study of physics beyond the Standard Model. Advances in these areas are often made even more compelling by their important implications for our understanding of the cosmology of the early universe, just as ideas from early universe cosmology broaden and enrich our attempts to answer those questions. This dissertation presents five related studies of particle physics phenomenology which exploit the fruitful interplay of these fields of research: (1) a detailed investigation of how dark matter annihilating to electroweak gauge and/or Higgs bosons, as described in a bottom-up approach via effective operators, can be constrained by indirect detection experiments that bound gamma-ray fluxes from the Galactic Centre and from nearby dwarf galaxies; (2) an examination of the direct detection and collider constraints that can be placed on the dimension-5 effective operators coupling fermionic dark-matter WIMPs to the Higgs Portal; (3) a study of the precision electroweak and Higgsstrahlung cross section constraints that a variety of proposed high-energy electron-positron colliders operating in the few-hundred GeV range can place on a simplified singlet-doublet model which UV completes the dimension-5 fermionic Higgs Portal; (4) a study of how the recently proposed cosmological relaxation mechanism can be used to generate the Little Hierarchy in a concrete composite Higgs model, and possible signatures of this framework; and finally, (5) a detailed numerical and analytical investigation of the irruptive production of late-time supermassive particles---a possible candidate for dark matter---during the inflationary epoch of the early universe, in models where those particles become momentarily light or tachyonic during inflation.


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