Interdependence between integrable cosmological models with minimal and non-minimal coupling

TL;DR

This paper explores the relationship between exact solutions of cosmological models with minimal and non-minimal scalar field couplings, revealing conditions for bounces and generalizations to different universe geometries.

Contribution

It demonstrates a connection between integrable cosmological models with different couplings and extends solutions to closed and open universes.

Findings

Existence of bounces in certain models

Generalization to closed and open universes

Conditions for integrability and simple dynamics

Abstract

We consider the relation between exact solutions of cosmological models having minimally and non-minimally coupled scalar fields. This is done for a particular class of solvable models which, in the Einstein frame, have potentials depending on hyperbolic functions and in the Jordan frame, where the non-minimal coupling is conformal, possess a relatively simple dynamics. We show that a particular model in this class can be generalized to the cases of closed and open Friedmann universes and still exhibits a simple dynamics. Further we illustrate the conditions for the existences of bounces in some sub-classes of the set of integrable models we have considered.