Non-Integrability and Chaos in Classical Cosmology

TL;DR

This paper investigates the dynamics of a cosmological model with a scalar field, demonstrating non-integrability and chaos through Painleve analysis, extending previous dynamical systems research.

Contribution

It applies Painleve theory to analyze cosmological equations, revealing non-integrability and chaotic behavior, thus advancing understanding of classical cosmology dynamics.

Findings

The system is generally non-integrable.

Chaos arises from movable logarithmic branch points.

Extends previous dynamical system analyses.

Abstract

A brief analysis of the dynamics of a Friedmann-Robertson-Walker universe with a conformally coupled, real, self-interacting, massive scalar field, based on the Painleve theory of differential equations, is presented. Our results complete earlier works done within the framework of Dynamical System Theory. We conclude that, in general, the system will not be integrable and that the chaos that has been found in a previous work, arises from the presence of movable logarithmic branch points in the solution in the complex plane of time.