  We consider a model of inflation consisting a single fluid with a
time-dependent equation of state. In this phenomenological picture, two periods
of inflation are separated by an intermediate non-inflationary stage which can
be either a radiation dominated, matter dominated or kinetic energy dominated
universe, respectively, with the equation of state $w=1/3$, 0 or 1. We consider
the toy model in which the change in $w$ happens instantaneously. Depending on
whether the mode of interest leaves the horizon before or after or between the
phase transitions, the curvature power spectrum can have non-trivial sinusoidal
modulations. This can have interesting observational implications for CMB
anisotropies and for primordial black-hole formation.
