Non-minimal inflation and the running spectral index

We study a class of models in which the inflaton is minimally coupled to gravity with a term f(R)φ2. We focus in particular on the case where f∼R2, and the expansion of the scale factor is driven by the usual potential energy, while the rolling of the inflaton is driven by the non-minimal coupling. We show that the power spectrum is in general blue, and the problem of getting a running spectral index is eased. However, the inflaton potential must have a large second derivative in order to get a large running.