Perturbation spectra from intermediate inflation

We investigate models of `intermediate' inflation, where the scale factor a (t) grows as a (t) =exp (At^f), 0<f<1, A constant. These solutions arise as exact analytic solutions for a given class of potentials for the inflaton. For a simpler class of potentials falling off as a power of they arise as slow-roll solutions, and in particular they include, for f=23, the class of potentials which give the Harrison-Zel'dovich spectrum. The perturbation spectral index n can be greater than unity on astrophysical scales. It is also possible to generate substantial gravitational waves while keeping the scalar spectrum close to scale invariance; this latter possibility performs well when confronted with most observational data.