Extended inflation and generalised scalar-tensor theories

Abstract

We study the class of Bergmann-Wagoner scalar-tensor theories from the viewpoint of dynamical systems theory. We relate this to the currently popular extended inflation models. We show that under a certain class of perturbation, these models are structurally stable (i.e., the global nature of the phase portrait of the dynamical system does not change); we also find a more general class of perturbations which make the system structurally unstable. The form of these pertubations is related to a possible potential term for the scalar field coupling to gravity.