  Observations of anisotropies in the cosmic microwave background by the
Wilkinson Microwave Anisotropy Probe suggest the possibility of oscillations in
the primordial density perturbation. Such deviations from the usually assumed
scale-free spectrum were predicted in the multiple inflation model wherein
`flat direction' fields undergo rapid phase transitions due to the breaking of
supersymmetry by the large vacuum energy driving inflation. This causes sudden
changes in the mass of the (gravitationally coupled) inflaton and interrupts
its slow roll. We calculate analytically the resulting modifications to the
density perturbation and demonstrate how the oscillations arise.
