Chaos in a closed Friedmann-Robertson-Walker universe: An imaginary approach

TL;DR

This paper investigates the transition to chaos in a closed Friedmann-Robertson-Walker universe with a scalar field by complexifying the universe's radius, revealing bifurcations that lead to non-collapsing cosmological solutions.

Contribution

It introduces an imaginary approach to analyze chaos in cosmological models, identifying bifurcations that enable non-collapsing universes, applicable to various models.

Findings

Existence of heteroclinic connections between manifolds and periodic orbits.

Identification of two bifurcations crucial for non-collapsing universes.

Methodology applicable to other cosmological models.

Abstract

In this work we study the existence of mechanisms of transition to global chaos in a closed Friedmann-Robertson-Walker universe with a massive conformally coupled scalar field. We propose a complexification of the radius of the universe so that the global dynamics can be understood. We show numerically the existence of heteroclinic connections of the unstable and stable manifolds to periodic orbits associated to the saddle-center equilibrium points. We find two bifurcations which are crucial in creating non-collapsing universes both in the real and imaginary version of the models. The techniques presented here can be employed in any cosmological model.