Supersymmetric small-field inflation with tribrid superpotentials

In this thesis, we study supersymmetric models of tribrid inflation and new inflation, both of which can be realized with a tribrid superpotential.
In the first part, we focus on tribrid inflation, deriving relations between cosmological observables and model parameters as well as providing guidelines for embedding tribrid inflation in realistic particle physics models. As an example application, we show how tribrid inflation can be realized in an explicit model of the leptonic flavour structure based on a discrete family symmetry, and how the production of topological defects after inflation can be avoided in such a model. Finally, we consider the possibility of generating the non-renormalizable operators of the tribrid superpotential at a sub-Planckian mass scale, which extends the applicability of tribrid inflation to some models with intermediate energy scales.
In the second part, we study new inflation with tribrid superpotentials. We first calculate the effects of the imaginary inflaton component on the primordial perturbations, which are generic for supersymmetric realizations of new inflation and not specific to the tribrid superpotential. Afterwards, we show how the tribrid superpotential coupling provides not only a mechanism for dynamically generating the initial conditions for new inflation, but also an effective inflaton decay channel for reheating after inflation. We also study the different preheating mechanisms in this setup and discuss under which conditions preheating can affect the final reheating phase.
In the last part, we consider whether small-field models of slow-roll inflation would remain viable if large primordial tensor perturbations were observed. In particular, we explain why such an observation would imply a scale dependent running of the spectral index, and we derive a general slow-roll bound to prove that an observation of tensor modes close to the current upper bound has the potential to rule out the entire framework of small-field slow-roll inflation employed throughout this thesis.