2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/181364We study a class of generalized inflation models in which the inflaton is coupled to the Ricci scalar by a general $f(ϕ, R)$ 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.26 pages, LaTeX; v2: refs. added; refs. correctedAstrophysicsGeneral Relativity and Quantum CosmologyHigh Energy Physics - Theorytext