  We present a number of new, exact scalar field cosmologies where the
potential consists of two or more exponential terms. Such potentials are
motivated by supergravity or superstring models formulated in higher
dimensional spacetimes that have been compactified to (3+1)-dimensions. We have
found solutions in both curved and flat Robertson Walker spacetimes. These
models have a diverse range of properties and often possess several distinct
phases, with a smooth transition between ordinary and inflationary expansion.
While exponential potentials typically produce powerlaw inflation, we find
models where the inflationary period contains eras of both powerlaw and
exponential growth.
