Extended Inflation with a Curvature-Coupled Inflaton

We examine extended inflation models enhanced by the addition of a coupling between the inflaton field and the space-time curvature. We examine two types of model, where the underlying inflaton potential takes on second-order and first-order form respectively. One aim is to provide models which satisfy the solar system constraints on the Brans--Dicke parameter $\omega$. This constraint has proven very problematic in previous extended inflation models, and we find circumstances where it can be successfully evaded, though the constraint must be carefully assessed in our model and can be much stronger than the usual $\omega > 500$. In the simplest versions of the model, one may avoid the need to introduce a mass for the Brans--Dicke field in order to ensure that it takes on the correct value at the present epoch, as seems to be required in hyperextended inflation. We also briefly discuss aspects of the formation of topological defects in the inflaton field itself.