Interactive mixture of inhomogeneous dark fluids driven by dark energy: a dynamical systems analysis

TL;DR

This paper analyzes the dynamics of an inhomogeneous dark matter and dark energy mixture using a Lemaître-Tolman-Bondi model, revealing stable early universe behavior and providing insights into structure formation.

Contribution

It introduces a dynamical systems framework for inhomogeneous dark fluid mixtures with interactions, extending previous models and analyzing phase space evolution.

Findings

Phase space trajectories are compatible with plausible early universe behavior.

The model admits stable past attractors for all parameter values.

Numerical examples illustrate structure formation scenarios.

Abstract

We examine the evolution of an inhomogeneous mixture of non-relativistic pressureless cold dark matter (CDM), coupled to dark energy (DE) characterised by the equation of state parameter $w<-1/3$, with the interaction term proportional to the DE density. This coupled mixture is the source of a spherically symmetric Lema\^\ itre-Tolman-Bondi (LTB) metric admitting an asymptotic Friedman-Lema\^\ itre-Robertson-Walker (FLRW) background. Einstein's equations reduce to a 5-dimensional autonomous dynamical system involving quasi--local variables related to suitable averages of covariant scalars and their fluctuations. The phase space evolution around the critical points (past/future attractors and five saddles) is examined in detail. For all parameter values and both directions of energy flow (CDM to DE and DE to CDM) the phase space trajectories are compatible with a physically plausible early cosmic times behaviour near the past attractor. This result compares favourably with mixtures with the interaction driven by the CDM density in which conditions for a physically plausible past evolution are more restrictive. Numerical examples are provided describing the evolution of an initial profile that can be associated with idealised structure formation scenarios