Extended Slow-Roll Conditions and Primordial Fluctuations: Multiple Scalar Fields and Generalized Gravity

As an extension of our previous study, we derive slow-roll conditions for multiple scalar fields which are non-minimally coupled with gravity and for generalized gravity theories of the form $f(\varphi ,R)$. We provide simple formulae of the spectral indices of scalar/tensor perturbations in terms of the slow-roll parameters.