In this project a recent model of inflation in which the Standard Model Higgs field with a nonminimal coupling to gravity takes on the role of the inflaton field is investigated. The tensor to scalar ratio, spectral index and the running of the spectral index  is calculated for a tree level analysis and compared with the Planck experiment. The value of the nonminimal coupling constant $\xi$ is estimated by obtaining a relation between the amplitude of scalar perturbations and the Higgs mass, it is found that $\xi \sim 10^4$. The basic aspects of how the results are modified through quantum corrections and what the consequences of the nonminimal coupling are for the effective field theory description is discussed. It is found that a tree level analysis yields predictions which are inside the allowed regions of the cosmological parameters given by the Planck experiment. The large value of the nonminimal coupling leads to unitarity problems for this model of inflation.  However quantum effects will have a significant effect and how they modify the results of the tree level analysis is what decides if Higgs inflation is a viable theory. / I detta projekt undersöker vi en modell av kosmisk inflation där Higgsfältet med en ickeminimal koppling till tyngdkraften är mekanismen bakom inflation. Vi utför en klassisk analys och beräknar modellens föresägelser för ett antal kosmologiska parametrar som jämförs med Planck experimentet. Vi uppskattar värdet på den ickeminimala kopplingen $\xi$ och finner att $\xi \sim 10^4$. De grundläggande aspekterna bakom kvantanalysen samt vad effekten av den ickeminimala kopplingen har på beskrivningen i termer av en effektiv fältteori diskuteras. Vi finner att en klassisk analys ger förutsägelser som passar väl med Planckexperimentet men att den ickeminimala kopplingen leder till unitaritetsproblem för denna modell av inflation. Kvanteffekter kan dock ha en avsevärd effekt på resultat och en utförlig analys som tar dem till hänsyn krävs för att avgöra om Higgsinflation är en möjlig modell för inflation.

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 right-handed neutrinos - and their possible solutions. The first issue is the tension between dark matter production in the nuMSM and constraints from the Lyman-alpha 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 left-right 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 ξ-inflation. In the vMSM, a large non-minimal 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 ξ-inflation with M_h ≃ 125-126 GeV, for which the Higgs self-coupling 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 ξ-inflation with a large tensor-to-scalar 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 Peccei-Quinn scalar S, whose couplings to the SM are ultra-weak, can solve the strong CP problem and generate electroweak symmetry breaking via the Coleman-Weinberg mechanism. The ultra-weak couplings of S are natural due to an underlying approξmate shift symmetry. The model contains a light pseudo-Goldstone 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.