Perturbation spectra from intermediate inflation

We investigate models of `intermediate' inflation, where the scale factor $a(t)$ grows as a(t)=exp(Atᶠ), $0<f<1$, A constant. These solutions arise as exact analytic solutions for a given class of potentials for the inflaton φ. For a simpler class of potentials falling off as a power of φ they arise as slow-roll solutions, and in particular they include, for f=2/3, 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.