Chaos in Preinflationary Friedmann-Robertson-Walker Universes

TL;DR

This paper investigates the chaotic dynamics of a preinflationary universe modeled by a closed Friedmann-Robertson-Walker geometry with radiation and a scalar field, revealing complex phase space structures and multiple inflationary exits.

Contribution

It introduces a detailed analysis of chaos in preinflationary cosmology using phase space topology, highlighting the role of homoclinic cylinders and non-integrability in the dynamics.

Findings

Chaotic behavior arises from homoclinic cylinders in phase space.

Multiple inflationary exits are associated with de Sitter attractors.

The system's non-integrability leads to complex, chaotic transitions from singularity to inflation.

Abstract

The dynamics of a preinflacionary phase of the universe, and its exit to inflation, is discussed. This phase is modeled by a closed Friedmann-Robertson-Walker geometry, the matter content of which is radiation plus a scalar field minimally coupled to the gravitational field. The simple configuration, with two effective degres of freedom only, presents a very complicated dynamics connected to the existence of critical points of saddle-center type and saddle type in phase space of the system. Each of these critical points is associated to an extremum of the scalar field potential. The Topology of the phase space about the saddle-center is characterized by homoclinic cylinders emanating from unstable periodic orbits, and the transversal crossing of the cylinders, due to the non-integrability of the system, results in a chaotic dynamics. The topology of the homoclinic cylinders provides an invariant characterization of chaos. The model exhibits one or more exits to inflation, associated to one or more strong asymptotic de Sitter attractors present in phase space, but the way out from the initial singularity into any of the inflationary exits is chaotic. We discuss possible mechanisms, connected to the spectrum of inhomogeneous fluctuations in the models, which would allow us to distinguish physically the several exits to inflation.