  At the end of inflation, the inflaton oscillates at the bottom of its
potential and these oscillations trigger a parametric instability for scalar
fluctuations with wavelength $\lambda$ comprised in the instability band $(3H
m)^{-1/2} <\lambda < H^{-1}$, where $H$ is the Hubble parameter and $m$ the
curvature of the potential at its minimum. This "metric preheating"
instability, which proceeds in the narrow resonance regime, leads to various
interesting phenomena such as early structure formation, production of
gravitational waves and formation of primordial black holes. In this work we
study its fate in the presence of interactions with additional degrees of
freedom, in the form of perturbative decay of the inflaton into a perfect
fluid. Indeed, in order to ensure a complete transition from inflation to the
radiation-dominated era, metric preheating must be considered together with
perturbative reheating. We find that the decay of the inflaton does not alter
the instability structure until the fluid dominates the universe content. As an
application, we discuss the impact of the inflaton decay on the production of
primordial black holes from the instability. We stress the difference between
scalar field and perfect fluid fluctuations and explain why usual results
concerning the formation of primordial black holes from perfect fluid
inhomogeneities cannot be used, clarifying some recent statements made in the
literature.
