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

Understand

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.