Sudden variations in the speed of sound during inflation: Features in the power spectrum and bispectrum

We employ the formalism of the effective field theory of inflation to study the effects of a sudden change in the speed of sound of the inflationary perturbations. Such an event generates a feature with high frequency oscillations both in the two-and in the three-point functions of the curvature fluctuations. We study, at first order in the magnitude of the change of the speed of sound, the dependence of the power spectrum and of the bispectrum on the duration of the change. In the limit of a very short duration, the oscillations in the power spectrum persist up to very large momenta and the amplitude of the feature in the bispectrum diverges while its location moves to increasing momenta.