Title:

The standard model to the Planck scale

The lack of direct evidence for physics beyond the SM at the LHC has led some to reevaluate the need for such physics to solve the hierarchy problem. Instead, the notion that the SM, or something like it, is valid up to the Planck scale and that technical naturalness is sufficient for solving the hierarchy problem has been suggested. This thesis examines minimal extensions of the SM that address its phenomenological and theoretical shortcomings while avoiding new physics between the electroweak and Planck scales that introduces a hierarchy problem. This thesis first studies two issues with the vMSM  an extension of the SM by three righthanded neutrinos  and their possible solutions. The first issue is the tension between dark matter production in the nuMSM and constraints from the Lymanalpha forest data. To avoid this tension, the vMSM is extended by a Higgs singlet Φ and neutrino dark matter is produced through the decays of Φ rather than through leftright neutrino mixing. It is shown that the hierarchical parameters of this model can arise from symmetries broken at or near the Planck scale for two specific examples: one in which Φ stabilizes the electroweak vacuum and one in which Φ is a light inflaton. The second issue pertains to Higgs ξinflation. In the vMSM, a large nonminimal coupling ξ of the Higgs to gravity gives inflation but leads to a possible violation of perturbative unitarity below the inflationary scale. A study of Higgs ξinflation with M_{h} ≃ 125126 GeV, for which the Higgs selfcoupling λ runs to small values near the Planck scale, is carried out. It is shown that small λ can significantly reduce ξ required for inflation, but ξ cannot be small enough to address the possible unitarity issue. For small λ, a new region of Higgs ξinflation with a large tensortoscalar ratio r that is consistent with BICEP2 is discovered. This thesis then studies the technical naturalness and cosmology of a model that addresses the strong CP problem. It is shown that a classically scale invariant DFSZ invisible aξon model with a PecceiQuinn scalar S, whose couplings to the SM are ultraweak, can solve the strong CP problem and generate electroweak symmetry breaking via the ColemanWeinberg mechanism. The ultraweak couplings of S are natural due to an underlying approξmate shift symmetry. The model contains a light pseudoGoldstone dilaton that can be consistent with cosmological bounds while the aξon can be the dark matter of the universe. Finally, a summary of the thesis is presented and future research topics are suggested.
