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 t
ransition which is needed to follow the fate of the perturbations is c
larified. We dissipate misleading statements made recently in the lite
rature concerning the predictions of the primordial fluctuations from
inflation and confirm standard results. Applications to string cosmolo
gy are considered.