Friedmann-Lema\^itre universes and their metamorphoses

TL;DR

This paper studies the dynamics of Friedmann-Lemaître universes, classifying their behaviors through bifurcation analysis, and describes stable, singularity-free solutions influenced by parameters beyond standard cosmology.

Contribution

It provides a comprehensive classification of universe evolutions via normal forms and bifurcations, introducing new parameters affecting cosmological dynamics.

Findings

Four main types of universe behaviors identified

Stable, singularity-free solutions characterized

Parameter-dependent solutions and transformations fully described

Abstract

We analyze the dynamics of the Friedmann-Lema\^itre universes taking into account the different roles played by the fluid parameter and the cosmological constant, as well as the degenerate character of the equations. We find that the Friedmann-Lema\^itre system reduces to four qualitatively inequivalent normal forms and write down the sets of all stable perturbations that may result (the `versal unfoldings'). These sets are of small codimension up to three. We then describe all possible parameter-dependent solutions and their transfigurations to other forms during evolution through the bifurcation sets, these are also fully described. This analysis leads to a picture of cosmological evolution determined by new parameters related to codimension which are zero in standard cosmology. The emerging versal solutions are all free of singularities, while other properties of them are also discussed.