Inflation during oscillations of the inflaton

Damour and Mukhanov have recently devised circumstances in which inflation may continue during the oscillatory phase which ensues once the inflaton field reaches the minimum of its potential. We confirm the existence of this phenomenon by numerical integration. In such circumstances the quantification of the amount of inflation requires particular care. We use a definition based on the decrease of the comoving Hubble length, and show that Damour and Mukhanov overestimated the amount of inflation occurring. We use the numerical calculations to check the validity of analytic approximations.