Classification of Inflationary Potentials

TL;DR

This paper classifies inflationary potentials within Brans-Dicke gravity based on the geometric area enclosed by inflation start and end curves, linking potential types to different cosmological outcomes and observational compatibility.

Contribution

It introduces a novel classification scheme for inflationary potentials based on the enclosed area between inflation boundaries in the scalar field plane.

Findings

Finite area potentials are compatible with our observable universe.

Infinite area potentials lead to different, less realistic cosmologies.

The classification distinguishes two fundamentally different classes of inflationary models.

Abstract

Brans-Dicke gravity is remarkable not only in that General Relativity and Mach's Principle find a common enlarged scenario where they are mutually consistent, but also in that it provides a very interesting quantum cosmological model within the inflationary paradigm. The interplay between the Brans-Dicke scalar $\Phi$ and the inflaton field $\sigma$ plays an important r\^{o}le during the course of inflation, and although the dynamics as such is governed by the potential, the onset and the end of inflation are determined by the values of both fields jointly. The relative position of the beginning-- and end-of-inflation curves (BoI and EoI respectively) is the most relevant factor in determining the resulting 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 qualitative classification distinguishes two classes of potentials that yield 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.