Steinwachs, Christian Friedrich

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Kölner UniversitätsPublikationsServer

Non-minimal Higgs Inflation and Frame Dependence in Cosmology

AbstractIn this thesis, we investigate the cosmological model of non-minimal Higgs infla-tion. The basic idea is to unify the “low-energy” sector of the Standard Modelwith the high-energy phase of inflation during the early universe. Both sectorsrely on the existence of a fundamental scalar field. The scalar Higgs boson is anintegral part of the Standard Model in order to maintain gauge invariance whileexplaining the origin of the masses of the elementary particles. Similar, in cosmol-ogy the scalar inflaton is necessary in order to drive inflation, the rapid acceleratedphase of expansion. The basic assumption of the Higgs inflation scenario is thatthe two scalar particles are only the manifestations of one and the same parti-cle, the “Higgs-inflaton”. The consistency with observational data of the cosmicbackground radiation requires the assumption of a strong non-minimal coupling ofthe Higgs-inflaton to gravity. It turns out that quantum corrections mainly deter-mine the cosmological parameters of the model and are crucial for the predictions.Moreover, we resort to the renormalization group flow in order to connect the en-ergy scale of the electroweak vacuum with the inflationary energy scale, separatedby many orders of magnitude. We derive a range of possible values for the massof the Higgs-inflaton. These predictions can be be tested by future experiments atthe Large Hadron Collider (LHC) and the satellite PLANCK.We further investigate an application of the non-minimal Higgs inflation modelin the context of quantum cosmology. Via the path integral approach, we calculatethe cosmological probability distribution for the universe to tunnel “from nothingto existence”. A sharp peak in this distribution - selecting a specific value ofthe inflaton field - can be interpreted as the initial conditions for inflation. Thepredicted value can be tested by the detection of primordial gravitational wavesthat leave their imprints in the B-polarization of the cosmic background radiation.In order to realize these models technically, we have calculated the divergent partof the one-loop off-shell effective action of a O(N)-symmetric multiplet of scalarfields non-minimally coupled to gravity in a closed form. Due to the functionalnature of the couplings, the result is very general and can be used as a referencefor many different cosmological applications.In cosmology, it is convenient to transform between two specific fieldparametrizations, denoted “Jordan frame” and “Einstein frame”. It is an ongoingdiscussion whether these two frames are physically equivalent. Mathematically,both frames are equivalent at the classical level. We explicitly show that thisdoes not hold anymore at the quantum level. Moreover, we identify this failureof equivalence to be part of a more general problem: the parametrization depen-dence of the conventional off-shell effective action. This reduces the cosmologicaldebate between Jordan frame and Einstein frame to the lack of covariance of theformalism.

Non-minimal Higgs Inflation and Frame Dependence in Cosmology

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