Inflation without Slow Roll

We draw attention to the possibility that inflation (i.e. accelerated expansion) might continue after the end of slow roll, during a period of fast oscillations of the inflaton field \phi . This phenomenon takes place when a mild non-convexity inequality is satisfied by the potential V(\phi). The presence of such a period of \phi-oscillation-driven inflation can substantially modify reheating scenarios. In some models the effect of these fast oscillations might be imprinted on the primordial perturbation spectrum at cosmological scales.