Phase-space analysis of the cosmological 3-fluid problem: Families of attractors and repellers

TL;DR

This paper analyzes the phase-space dynamics of a cosmological model with three fluids, revealing new attractors and repellers, and identifying conditions for various late-time behaviors including coexistence of dark energy and dark matter.

Contribution

It introduces new families of attractors and repellers in the three-fluid cosmological model, expanding understanding of late-time cosmic evolution.

Findings

Discovery of new attractors with dark energy and dark matter coexistence

Identification of saddle points and repellers in the phase space

A solution exhibiting multiple transient acceleration and deceleration periods

Abstract

We perform a phase-space analysis of the cosmological 3-fluid problem consisting of a barotropic fluid with an equation-of-state parameter $\gamma-1$, a pressureless dark matter fluid, plus a scalar field $\phi$ (representing dark energy) coupled to exponential potential $V=V_0\exp{(-\kappa\lambda\phi)}$. Besides the potential-kinetic-scaling solutions, which are not the unique late-time attractors whenever they exist for $\lambda^2\geq 3\ga$, we derive new attractors where both dark energy and dark matter coexist and the final density is shared in a way independent of the value of $\gamma >1$. The case of a pressureless barotropic fluid ($\gamma =1$) has a one-parameter family of attractors where all components coexist. New one-parameter families of matter-dark matter saddle points and kinetic-matter repellers exist. We investigate the stability of the ten critical points by linearization and/or Lyapunov's Theorems and a variant of the theorems formulated in this paper. A solution with two transient periods of acceleration and two transient periods of deceleration is derived.