Attempts at building a unified description of the strong, weak and electromagnetic interactions usually involve several stages of spontaneous symmetry breaking. We consider the effects of such symmetry breaking during an era of primordial inflation in supergravity models. In cases that these occur along flat directions at intermediate scales there will be a succession of short bursts of inflation which leave a distinctive signature in the spectrum of the generated scalar density perturbation. Thus measurements of the spectral index can directly probe the structure of unified theories at very high energy scales. An observed feature in the power spectrum of galaxy clustering from the APM survey may well be associated with such structure. If so, this implies a characteristic suppression of the secondary Doppler peaks in the angular power spectrum of temperature fluctuations in the cosmic microwave background.