The Higgs Boson and the Cosmos

The Higgs boson is a cornerstone of the standard model (SM) of particle physics, thus it comes as no surprise that the announcement of its discovery on July 2012 by ATLAS and CMS marked a very important date for particle physics. All the pieces of the SM have finally been observed and the parameters of the theory measured. However, we know that the SM is far from a complete theory and the fact that the Higgs boson has been, up to date, the only discovery of the LHC may be seen as unfortunate by many. In fact, the LHC is just confirming with exceptional accuracy the predictions of the SM, pushing the scale of new physics to larger and larger values, giving us no hints about its correct extension. Having measured all the parameters of the SM we can assume its validity to an arbitrarily high energy scale and extrapolate its behavior using the renormalization group equations. It turns out that the value of the Higgs mass is low enough to allow this extrapolation and the SM remains consistent up to the Planck scale. However, this computation reveals yet another puzzle: our universe does not lie in the global minimum of the Higgs potential; instead a much deeper vacuum exists at large field values. In principle, quantum tunneling into the true vacuum is possible but fortunately the decay time is much longer than the age of our universe. For all practical purposes our vacuum is not in danger and the decay will not happen any time soon. This peculiar situation is called metastability. Since the decay time is very long, new physics modifying the Higgs potential at high energies is not needed. The situation, however, changes dramatically if we want to understand why the Higgs ended up in such an energetically disfavored state in the framework of big bang cosmology. It is clear that some sort of fine-tuning is required in order to put the Higgs in the false vacuum. Not only that: the evolution of the universe goes through violent periods, such as inflation and reheating, where the Higgs may experience large fluctuations, making it difficult to justify why it did not decay into the true vacuum without assuming the existence of physics beyond the SM (BSM). The Higgs is a natural window into particles which are not part of the SM. In fact, it is the only particle with spin-0 and the only field which can form a dimension-2 gauge and Lorentz invariant operator. Within the SM this property is used to write a mass term for the Higgs which generates spontaneous breaking of the electroweak symmetry, while in BSM models it allows to write interaction terms at the renormalizable level with gauge singlets and with gravity. In this thesis and in the papers attached we explore the effects that these renormalizable BSM operators have on the Higgs dynamics in the early universe. We show that stabilization of the Higgs field can be obtained in models of inflation if we allow the existence of Higgs-inflaton couplings or non-minimal coupling with gravity. The same models are then studied at the reheating stage, when all the particles that compose the present day universe are produced. On the other hand, we also explore the possibility that the Higgs mixes with the inflaton. The mixing can stabilize the Higgs potential at all energies and generates two scalar eigenstates. The lighter one is identified with the boson discovered in 2012 and the other could be observed at the LHC or at future colliders