  We derive the matching conditions for cosmological perturbations in a
Friedmann Universe where the equation of state undergoes a sharp jump, for
instance as a result of a phase transition. The physics of the transition which
is needed to follow the fate of the perturbations is clarified. We dissipate
misleading statements made recently in the literature concerning the
predictions of the primordial fluctuations from inflation and confirm standard
results. Applications to string cosmology are considered.
