  Toy models for the Hubble rate or the scalar field potential have been used
to analyze the amplification of scalar perturbations through a smooth
transition from inflation to the radiation era. We use a Hubble rate that
arises consistently from a decaying vacuum cosmology, which evolves smoothly
from nearly de Sitter inflation to radiation domination. We find exact
solutions for super-horizon perturbations (scalar and tensor), and for
sub-horizon perturbations in the vacuum- and radiation-dominated eras. The
standard conserved quantity for super-horizon scalar perturbations is exactly
constant for growing modes, and zero for the decaying modes.
