CLASSIFICATION OF EXTENDED CHAOTIC INFLATION POTENTIALS

Brans-Dicke gravity is remarkable not only in that General Relativity and Mach's Principle find a common enlarged scenario where they are mu tually consistent, but also in that it provides a very interesting qua ntum cosmological model within the inflationary paradigm. The interpla y between the Brans-Dicke scaler Phi and the inflaton field sigma play s an important role during the course of inflation, and although the d ynamics as such is governed by the potential, the onset and the end of inflation are determined by the values of both fields jointly. The re lative position of the beginning - and end-of-inflation curves (BoI an d EoI respectively) is the most relevant factor in determining the res ulting quantum cosmological scenario. The classification of potentials that is given in this paper is based on the criterion of whether the BoI and EoI boundaries enclose a finite or infinite area in the (sigma , Phi) plane where inflation takes place. It is shown that this qualit ative classification distinguishes two classes of potentials that yiel d very different cosmologies and it is argued that only those theories in which BoI and EoI enclose a finite area in the (sigma, Phi) plane are compatible with our observable universe. (C) 1998 Elsevier Science B.V. All rights reserved.