  Recently, we presented a unified way of analysing classical cosmological
perturbation in generalized gravity theories. In this paper, we derive the
perturbation spectrums generated from quantum fluctuations again in unified
forms. We consider a situation where an accelerated expansion phase of the
early universe is realized in a particular generic phase of the generalized
gravity. We take the perturbative semiclassical approximation which treats the
perturbed parts of the metric and matter fields as quantum mechanical
operators. Our generic results include the conventional power-law and
exponential inflations in Einstein's gravity as special cases.
