  Inflationary cosmology provides a successful paradigm for solving several
problems, notably the generation of density perturbations which seed the
formation of observed cosmic structure. We show how to use inverse scattering
theory as the basis for the inflationary reconstruction program, the goal of
which is to gain information about the physics which drives inflation. Inverse
scattering theory provides an effective and well-motivated procedure, having a
sound mathematical basis and being of sufficient generality that it can be
considered the foundation for a non-parametric reconstruction program. We show
how simple properties of the power spectrum translate directly into statements
about the evolution of the background geometry during inflation.
