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The curvaton scenario predicts an almost scale-invariant spectrum ofperturbations in most inflation models. We consider the possibility thatrenormalisable phi^4 or Planck scale-suppressed non-renormalisable curvatonpotential terms may result in an observable deviation from scale-invariance. Weshow that if the curvaton initially has a large amplitude and if the totalnumber of e-foldings of inflation is less than about 300 then a running blueperturbation spectrum with an observable deviation from scale-invariance islikely. D-term inflation is considered as an example with a potentially lowtotal number of e-foldings of inflation. A secondary role for the curvaton, inwhich it drives a period of chaotic inflation leading to D-term or other flatpotential inflation from an initially chaotic state, is suggested.Comment: 12 pages LaTeX, minor corrections, to be published in JCA

Curvaton potential terms, scale-dependent perturbation spectra and chaotic initial conditions