Ten scenarios from early radiation to late time acceleration with a minimally coupled dark energy

TL;DR

This paper analyzes possible evolutionary sequences of the universe with dark energy using dynamical systems, identifying ten new viable sequences that avoid singularities in the dark energy equation of state.

Contribution

It introduces ten novel sequences of cosmic evolution with dark energy, derived through dynamical system analysis, avoiding singularities in the equation of state.

Findings

Ten sequences of universe evolution without singularities in w.

Most sequences are new in dark energy research.

Singular w points are necessary for additional sequences.

Abstract

We consider General Relativity with matter, radiation and a minimally coupled dark energy defined by an equation of state w. Using dynamical system method, we find the equilibrium points of such a theory assuming an expanding Universe and a positive dark energy density. Two of these points correspond to classical radiation and matter dominated epochs for the Universe. For the other points, dark energy mimics matter, radiation or accelerates Universe expansion. We then look for possible sequences of epochs describing a Universe starting with some radiation dominated epoch(s) (mimicked or not by dark energy), then matter dominated epoch(s) (mimicked or not by dark energy) and ending with an accelerated expansion. We find ten sequences able to follow this Universe history without singular behaviour of w at some saddle points. Most of them are new in dark energy literature. To get more than these ten sequences, w has to be singular at some specific saddle equilibrium points. This is an unusual mathematical property of the equation of state in dark energy literature, whose physical consequences tend to be discarded by observations. This thus distinguishes the ten above sequences from an infinity of ways to describe Universe expansion.