Classification of Inflationary Einstein--Scalar--Field--Models via Catastrophe Theory

TL;DR

This paper introduces a new method using catastrophe theory and Hubble parameter reparametrization to classify inflationary scalar field potentials and analyze their stability, encompassing all known exact solutions.

Contribution

It presents a novel classification approach for inflationary potentials based on catastrophe theory, unifying known solutions and linking critical point behavior to cosmic reheating.

Findings

Classified inflationary potentials using catastrophe theory.

Connected critical point coalescence to reheating phase.

Provided examples illustrating the classification scheme.

Abstract

Various scenarios of the initial inflation of the universe are distinguished by the choice of a scalar field {\em potential} $U(\phi)$ which simulates a {\it temporarily} non--vanishing {\em cosmological term}. Our new method, which involves a reparametrization in terms of the Hubble expansion parameter $H$, provides a classification of allowed inflationary potentials and of the stability of the critical points. It is broad enough to embody all known {\it exact} solutions involving one scalar field as special cases. Inflation corresponds to the evolution of critical points of some catastrophe manifold. The coalescence of its nondegenerate critical points with the creation of a degenerate critical point corresponds the reheating phase of the universe. This is illustrated by several examples.