Autonomous Dynamical System of Einstein-Gauss-Bonnet Cosmologies

TL;DR

This paper explores the complex phase space of Einstein-Gauss-Bonnet cosmological models, identifying equilibrium points, invariant structures, and a heteroclinic orbit that influences the universe's evolution, revealing rich dynamics and physical constraints.

Contribution

It provides a detailed phase space analysis of Einstein-Gauss-Bonnet cosmologies, highlighting invariant structures and the existence of heteroclinic orbits affecting cosmological evolution.

Findings

Existence of a stable equilibrium point with physical significance.

Identification of invariant manifolds influencing system dynamics.

Discovery of a heteroclinic orbit connecting different cosmological states.

Abstract

In this paper, we study the phase space of cosmological models in the context of Einstein-Gauss-Bonnet theory. More specifically, we consider a generalized dynamical system that encapsulates the main features of the theory and for the cases that this is rendered autonomous, we analyze its equilibrium points and stable and unstable manifolds corresponding to several distinct cosmological evolutions. As we demonstrate, the phase space is quite rich and contains invariant structures, which dictate the conditions under which the theory may be valid and viable in describing the evolution Universe during different phases. It is proved that a stable equilibrium point and two invariant manifolds leading to the fixed point, have both physical meaning and restrict the physical aspects of such a rich in structure modified theory of gravity. More important we prove the existence of a heteroclinic orbit which drives the evolution of the system to a stable fixed point. However, while on the fixed point the Friedman constraint corresponding to a flat Universe is satisfied, the points belonging to the heteroclinic orbit do not satisfy the Friedman constraint. We discuss the origin of this intriguing issue in some detail.