Higgs Vacuum Stability, Inflation & Physics Beyond the Standard Model

The discovery of the Higgs particle, simultaneous measurement of it's mass and subsequent confirmation of it's status as the Standard Model (SM) Higgs represents the completion of the theory in it's original guise. Armed with all necessary inputs of the theory at the weak scale, it is now possible to extrapolate the parameters of the theory up to the Planck scale. We complement the current state of the art renormalisation group (RG) studies performed in the MS bar scheme with an analogous study performed in an explicitly mass-dependant scheme. The necessary renormalisation and construction of the mass-dependent beta--functions is performed. We then RG evolve the SM parameters up to the planck scale and, in parallel to the current studies, find the electroweak (EW) symmetry breaking Higgs vacuum to be metastable, but with increased statistical significance as compared to those studies, we also find a reduction of the errors in the theoretical determination of the critical values of the Higgs and top pole masses required for absolute stability of the SM Higgs vacuum. An ever-growing body of evidence supports the idea of a period of exponential inflation in the early history of the universe. The non-flat spacetime geometry during inflation gives rise to new decay mechanisms not considered in the flat spacetime analysis of SM Higgs vacuum decay. We re-examine stability of the SM Higgs vacuum during inflation, finding new instantons with no flat-spacetime analogue dominate in the decay. Under the assumption of no new physics beyond the SM and forcing the requirement that inflation should proceed, we are able to place a bound upon the inflationary rate. Combining our results with the most likely value of the rate of inflation suggested by combination of the Planck and BICEP2 measurements of the CMB temperature anisotropy, we find the SM Higgs vacuum could not have survived inflation, providing new evidence for physics beyond the SM Motivated by the need for new physics which should stabilise the Higgs potential, we discuss the effect of adding new degrees of freedom and interactions to the SM, first in a general context, but then looking at concrete examples, focussing on the effect of models which could explain the mechanism of neutrino mass generation. We find the parameter space in type-II seesaw models to be the least constrained by the requirement of vacuum stability, thanks to the introduction of new bosonic, rather than fermionic, degrees of freedom. Finally, we consider the apparently accidental near criticality of the Higgs potential and find that it is possible to provide an explanation for this phenomenon using the framework of classically scale invariant models. We construct an explicit example of such a model, finding the symmetries of the theory permit a reduction in the number of free parameters of the SM by one