We consider the consequences of an observed Cosmic Microwave Background (CMB)
temperature anisotropy spectrum containing no secondary oscillations. While
such a spectrum is generally considered to be a robust signature of active
structure formation, we show that such a spectrum {\em can} be produced by
(very unusual) inflationary models or other passive evolution models. However,
we show that for all these passive models the characteristic oscillations would
show up in other observable spectra. Our work shows that when CMB polarization
and matter power spectra are taken into account secondary oscillations are
indeed a signature of even these very exotic passive models. We construct a
measure of the observability of secondary oscillations in a given experiment,
and show that even with foregrounds both the MAP and \pk satellites should be
able to distinguish between models with and without oscillations. Thus we
conclude that inflationary and other passive models can {\em not} evade the
secondary oscillation test.Comment: Final version accepted for publication in PRD. Minor improvements
have been made to the discussion and new data has been included. The
conclusions are unchagne
