  Type-II seesaw leptogenesis is a model that integrates inflation, baryon
number asymmetry, and neutrino mass simultaneously. It employs the Affleck-Dine
mechanism to generate lepton asymmetry, with the Higgs bosons serving as the
inflaton. Previous studies assumed inflation to occur in a valley of the
potential, employing the single-field approximation. In this work, we explore
an alternative scenario for the type-II seesaw leptogenesis, where the
inflation takes place along a ridge of the potential. Firstly, we conduct a
comprehensive numerical calculation in the canonical scenario, where inflation
occurs in a valley, confirming the effectiveness of the single-field
approximation. Then, we introduce a novel scenario wherein inflation initiates
along the potential's ridge and transitions to the valley in the late stages.
In this case, the single-field inflation approximation is no longer valid, yet
leptogenesis is still successfully achieved. We find that this scenario can
generate a significant non-Gaussianity signature, offering testable predictions
for future experiments.
