Curvature perturbation at the local extremum of the inflaton potential

Abstract

The spectrum of curvature perturbation generated during inflation is studied in the case the inflation-driving scalar field (inflaton) $\phi$ crosses over its potential extremum. It is shown that the nondecaying mode of perturbation has a finite value and a proper formula is given. The result is also extended to more general cases where $\ddot{\phi}$ is non-negligible.