I show that cosmological perturbation spectra produced from quantum fluctua
tions in massless or self-interacting scalar fields during an inflationary
era remain invariant under a two parameter family of transformations of the
homogeneous background fields. This relates slow-roll inflation models to
solutions which may be far from the usual slow-roll limit. For example, a s
cale-invariant spectrum of perturbations in a minimally coupled, massless f
ield can be produced by an exponential expansion with a proportional to e(H
t), or by a collapsing universe with a proportional to(- t)(2/3). [S0556-28
21(99)02814-3].