  We analyze the general conditions on the equation of state $w$ required for
quantum fluctuations of a scalar field to produce a scale-invariant spectrum of
density perturbations, including models which (in the four dimensional
effective description) bounce from a contracting to an expanding phase. We show
that there are only two robust cases: $w\approx -1$ (inflation) and $w \gg 1$
(the ekpyrotic/cyclic scenario). All other cases, including the $w \approx 0$
case considered by some authors, require extreme fine-tuning of initial
conditions and/or the effective potential. For the ekpyrotic/cyclic ($w \gg 1$)
case, we also analyze the small deviations from scale invariance.
