Einstein's Field Equations as a Fold Bifurcation

TL;DR

This paper demonstrates that Einstein's field equations for flat FLRW cosmologies can be understood as a fold bifurcation, revealing how de Sitter universes emerge through bifurcation as the cosmological constant varies.

Contribution

It establishes a novel connection between Einstein's equations and bifurcation theory, specifically showing the equations' normal form as a fold bifurcation.

Findings

Fold bifurcation behavior occurs near Minkowski spacetime.

Expanding and contracting de Sitter universes emerge via bifurcation.

The cosmological constant acts as a bifurcation parameter.

Abstract

It is shown that Einstein's field equations for \emph{all} perfect-fluid $k=0$ FLRW cosmologies have the same form as the topological normal form of a fold bifurcation. In particular, we assume that the cosmological constant is a bifurcation parameter, and as such, fold bifurcation behaviour is shown to occur in a neighbourhood of Minkowski spacetime in the phase space. We show that as this cosmological constant parameter is varied, an expanding and contracting de Sitter universe \emph{emerge} via this bifurcation.