Multi-field open inflation model and multi-field dynamics in tunneling

We consider a multi-field open inflation model, in which one of the fields dominates quantum tunneling from a false vacuum while the other field governs slow-roll inflation within the bubble nucleated from false vacuum decay. We call the former the tunneling field and the latter the inflaton field. In the limit of a negligible interaction between the two fields, the false vacuum decay is described by a Coleman-De Luccia instanton. Here we take into account the coupling between the two fields and construct explicitly a multi-field instanton for a simple quartic potential model. We also solve the evolution of the scalar fields within the bubble. We find our model realizes open inflation successfully. This is the first concrete, viable model of open inflation realized with a simple potential. We then study the effect of the multi-field dynamics on the false vacuum decay, specifically on the tunneling rate. We find the tunneling rate increases in general in comparison with the single field case, though the increase is small unless the inflaton affects the instanton solution substantially.