Density spectra from pole-like inflations based on generalized gravity theories

We present a general and unified formulation which can handle the classical evolution and quantum generation processes of cosmological scalar-type perturbations in a broad class of generalized gravity theories. Applications are made to the pole-like accelerated expansion stages purely driven by the coupling between the gravity and the dilaton field without referring to the potential term which are realized in a class of generalized gravity theories. We consider three such scenarios based on the scalar-tensor gravity, the induced gravity and the string theory. Vacuum fluctuations during the several expansion stages can be derived in exact analytic forms. Assuming that the pole-like acceleration stage provides a viable inflation scenario in the early universe, and assuming that the gravity theory transits to an Einstein one while the relevant scales remain in the superhorizon scale, we derive the generated classical density spectra. The generated classical density field shows a generic tilted spectrum with which differs from the observed spectrum supporting .