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

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 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.

Bouncing universe in the contexts of generalized cosmic Chaplygin gas and variable modified Chaplygin gas

“…Inhomogeneous dust with a positive cosmological constant given by the Lema ître-Tolman-Bondi (LTB) model was investigated in [74] and the critical points were examined in a unique way. Further recent studies in the inhomogeneous sector was conducetd with interactive mixture of dark fluids [75]. Interactive holographic dark energy models were explored in the light of stability analysis in Einstein's gravity [76] and other theories of gravity [77].…”

Large-scale (in) stability analysis of an exactly solved coupled dark-energy model

“…We also mention that the evolution of an inhomogeneous mixture of nonrelativistic pressureless CDM, coupled to DE in which the interaction term proportional to the DE density was studied in Ref. [60]. Here, from the spherically symmetric Lemaître-Tolman-Bondi metric, the authors found that the interaction Q can be written as Q ∝ρ x as used in [23].…”

“…For a comprehensive review on different interaction rates, we refer to [57,58]. We also note that the interaction between the dark sectors has also been examined in a more general framework where the geometry of the universe is inhomogeneous [59,60].…”

Evolution equations dynamical system of the Lemaître--Tolman--Bondi metric containing coupled dark energy

“…We have studied previously LTB metric models by means of the QL formalism [28,23,25,26,30,31,32], more recently considering as sources mixtures of nonrelativistic CDM, described as dust, coupled to DE described as a dark fluid with constant equation of state w < −1/3. In [30] we assumed the coupling term to be proportional to CDM energy density, while in [31] it was proportional to the DE density.…”

“…We have studied previously LTB metric models by means of the QL formalism [28,23,25,26,30,31,32], more recently considering as sources mixtures of nonrelativistic CDM, described as dust, coupled to DE described as a dark fluid with constant equation of state w < −1/3. In [30] we assumed the coupling term to be proportional to CDM energy density, while in [31] it was proportional to the DE density. In the present article we generalize these previous results by considering a coupling term proportional to the sum energy densities of both dark sources, considering as well a contribution of a baryonic matter source.…”