Sanderson, Jennifer (1999) Aspects of hybrid inflation in supersymmetry. University of Southampton, Doctoral Thesis.
Abstract
Details of the hybrid inflation scenario have been studied in the context of the standard non-supersymmetric hybrid potential, its (F-term) SUSY form, and its role within a specific SUSY model, the φNMSSM. A particularly appealing variant of the standard hybrid mechanism, inverted hybrid inflation, is found to be unnatural , requiring coupling constants in the potential 10-12. It is also very difficult to achieve a SUSY model of inverted hybrid inflation with one suggested superpotential unbounded from below. The φNMSSM provides a realistic SUSY model capable of both hybrid and inverted hybrid inflation and we study the effects of preheating in this model and the general SUSY case. A particular behaviour is found to result, characteristic of the SUSY version of hybrid inflation, whereby there exists only one natural frequency of coherent homogeneous fields. An analytical study of the parametric amplification via the Mathieu equation is found where the solutions depend on time, tracing a trajectory over each classical field oscillation through the instability chart and confirming the numerical results obtained. Production of axions is model dependent, but in the φNMSSM the dangerously amplified production which would occur considering the fields separately is sufficiently suppressed by proper inclusion of the mixing between the fields. The enormous numbers of the classical fields produced serve to shut off further production, quickly ending the preheating process via back reaction effects, thus leaving the axions safely within experimental bounds of the φNMSSM a viable model.
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