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 rho. This phenomenon rakes place when a mild nonconvexity inequality is satisfied by the potential V (rho). The presence of such a period of rho-oscillation-driven inflation can substantially modify reheating scenarios. In some models the effect of these fast oscillations might be imprinted on the primordial perturbation specrtrum at cosmological scales.