Curvature and entropy perturbations in generalized gravity

Abstract

We investigate the cosmological perturbations in generalized gravity, where the Ricci scalar and a scalar field are nonminimally coupled via an arbitrary function $f(\ensuremath{\varphi},R)$. In the Friedmann-Lema\^{\i}tre-Robertson-Walker background, by studying the linear perturbation theory, we separate the scalar-type perturbations into the curvature perturbation and the entropy perturbation, whose evolution equations are derived. Then we apply this framework to inflation. We consider the generalized slow-roll conditions and the quantization initial condition. Under these conditions, two special examples are studied analytically. One example is the case with no entropy perturbation. The other example is a model with the entropy perturbation large initially but decaying significantly after crossing the horizon.