We study a class of generalized inflation models in which the inflaton is
coupled to the Ricci scalar by a general f(Ï•,R) term. The scalar power
spectrum, the spectral index, the running of the spectral index, the tensor
mode spectrum and a new consistency relation of the model are calculated. We
discuss in detail the issues of how to diagonize the coupled perturbation
equations, how to deal with an entropy-like source, and how to determine the
initial condition by quantization. By studying some explicit models, we find
that rich phenomena such as a blue scalar power spectrum, a large running of
the spectral index, and a blue tensor mode spectrum can be obtained.Comment: 26 pages, LaTeX; v2: refs. added; refs. correcte