Oscillations in the inflaton potential?

We consider a class of inflationary models with small oscillations imprinted on an otherwise smooth inflaton potential. These oscillations are manifest as oscillations in the power spectrum of primordial perturbations, which then give rise to oscillating departures from the standard cosmic microwave background power spectrum. We show that current data from the Wilkinson Microwave Anisotropy Probe constrain the amplitude of a sinusoidal variation in the inflaton potential to have an amplitude less than 3 x 10^{-5}. We anticipate that the smallest detectable such oscillations in Planck will be roughly an order of magnitude smaller, with slight improvements possible with a post-Planck cosmic-variance limited experiment.