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Kostka, Philipp (2010): Particle Physics Models of Inflation in Supergravity and Grand Unification. Dissertation, LMU München: Faculty of Physics
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Abstract

In the first part of this thesis, we study classes of hybrid and chaotic inflation models in four-dimensional N=1 supergravity. Therein, the eta-problem can be resolved relying on fundamental symmetries in the Kaehler potential. Concretely, we investigate explicit realizations of superpotentials, in which the flatness of the inflaton potential is protected at tree level by a shift symmetry or a Heisenberg symmetry in the Kaehler potential. In the latter case, the associated modulus field can be stabilized during inflation by supergravity effects. In the context of hybrid inflation, a novel class of models, to which we refer as "tribrid inflation," turns out to be particularly compatible with such symmetry solutions to the eta-problem. Radiative corrections due to operators in the superpotential, which break the respective symmetry, generate the required small slope of the inflaton potential. Additional effective operators in the Kaehler potential can reduce the predicted spectral index so that it agrees with latest observational data. Within a model of chaotic inflation in supergravity with a quadratic potential, we apply the Heisenberg symmetry to allow for viable inflation with super-Planckian field values, while the associated modulus is stabilized. We show that radiative corrections are negligible in this context. In the second part, the tribrid inflation models are extended to realize gauge non-singlet inflation. This is applied to the matter sector of supersymmetric Grand Unified Theories based on the Pati-Salam gauge group. For the specific scenario in which the right-handed sneutrino is the inflaton, we study the scalar potential in a D-flat valley. We show that despite potentially dangerous two-loop corrections, the required flatness of the potential can be maintained. The reason for this is the strong suppression of gauge interactions of the inflaton field due to its symmetry breaking vacuum expectation value. In addition, the production of stable magnetic monopoles at the end of the stage of inflation can be avoided. Finally, we sketch how in tribrid inflation models the concepts discussed in the two parts can be combined to realize inflation via Heisenberg symmetry in local supersymmetric SO(10) grand unification.