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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.
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