Perturbation Spectra from Intermediate Inflation

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