A pr 1 99 9 Some remarks on Oscillating Inflation

In a recent paper Damour and Mukhanov describe a scenario where inflation may continue during the oscillatory phase. This effect is possible because the scalar field spends a significant fraction of each period f oscillation on the upper part of the potential. Such additional period of inflation could push perturbations after the slow roll regime to observable scales. Although we show that the small region of the Damour-Mukhanov parameter q gives the main contribution to oscillating inflation, it remained until now not satisfactory understood. Further, it drives to an expression for the energy density spectrum of perturbations, which is well behaved in the whole physical range of q .