Summary and Outlook

Abstract

In this thesis, we have investigated the model of non-minimal Higgs inflation. The unified description of the Standard Model Higgs boson and the cosmological inflaton required a strong non-minimal coupling to gravity. In order to ensure consistency with the data of the cosmic microwave background radiation, we could derive a numerical constraint for the mass of the Higgs-inflaton. We have used the results of the non-minimal Higgs inflation scenario in a quantum cosmological tunnelling scenario. Within a path integral formulation, we have calculated the probability distribution of the universe to tunnel from “nothing into existence”. We have found a sharp peak in this distribution, corresponding to a specific value of the inflaton field that can be interpreted as the initial condition for inflation. This quantum cosmological prediction of the model could possibly be tested in the near future by the analysis of primordial gravitational waves that leave their imprint in the B-polarization of the cosmic microwave background radiation. We have calculated the one-loop divergences for a very general cosmological model with arbitrary functional couplings and $N$ scalar fields non-minimally coupled to gravity in the Jordan frame parametrization. We found that already the first quantum corrections induce a frame dependence. The cosmological debate “Jordan frame” versus. “Einstein frame” is discussed from a new geometrical viewpoint.