https://doi.org/10.1140/epjc/s10052-018-5699-y
Regular Article - Theoretical Physics
Interactive mixture of inhomogeneous dark fluids driven by dark energy: a dynamical system analysis
1
Facultad de Ciencias, Universidad Autónoma del Estado de México, Instituto Literario 100, Estado de México, 5000, Toluca, México
2
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México (ICN-UNAM), A. P. 70–543, 04510, México D. F., Mexico
* e-mail: gizquierdos@uaemex.mx
Received:
23
November
2017
Accepted:
2
March
2018
Published online:
19
March
2018
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 
, with the interaction term proportional to the DE density. This coupled mixture is the source of a spherically symmetric Lemaître–Tolman–Bondi (LTB) metric admitting an asymptotic Friedman–Lemaître–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 interaction driven by the CDM density, whose past evolution is unphysical for DE to CDM energy flow. Numerical examples are provided describing the evolution of an initial profile that can be associated with idealised structure formation scenarios.
© The Author(s), 2018
