Dynamics of a spherically symmetric inhomogeneous coupled dark energy model with coupling term proportional to non relatvistic matter

Abstract

Abstract. Quasi-local scalar variables approach is applied to a spherically symmetric inhomogeneous Lemaître-Tolman-Bondi metric containing a mixture of non-relativistic cold dark matter and coupled dark energy with constant equation of state. The quasi-local coupling term considered is proportional to the quasi-local cold dark matter energy density and a quasi-local Hubble factor-like scalar via a coupling constant α. The autonomous numerical system obtained from the evolution equations is classified for different choices of the free parameters: the adiabatic constant of the dark energy w and α. The presence of a past attractor in a non-physical region of the energy densities phase-space of the system makes the coupling term non physical when the energy flows from the matter to the dark energy in order to avoid negative values of the dark energy density in the past. On the other hand, if the energy flux goes from dark energy to dark matter, the past attractor lays in a physical region. The system is also numerically solved for some interesting initial profiles leading to different configurations: an ever expanding mixture, a scenario where the dark energy is completely consumed by the nonrelativistic matter by means of the coupling term, a scenario where the dark energy disappears in the inner layers while the outer layers expand as a mixture of both sources, and, finally, a structure formation toy model scenario, where the inner shells containing the mixture collapse while the outer shells expand.PACS numbers: 98.80.-k, 04.20.-q, 95.36.+x, 95.35.+d

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

“…Hence, a comparison between our results and those of [44] suggests that the DE driven mixture should be favoured, as it exhibits a wider parameter consistency with a past evolution compatible with observations. The plan of the article is summarised as follows.…”

“…Following the methodology described in [42,43] (summarised in [44]), we consider a LTB metric in a comoving frame given by…”

“…As opposed to the system in [44], the past attractor is now fixed and the future attractor depends on the choice of parameters α and w. Thus, regardless of the sign of α (directionality of interaction energy flow), the past evolution is now a physically plausible CDM dominated scenario (compatible with observations) while the position of the future attractor describes various plausible DE dominated sce-narios that depend on the parameter choices. For α < 0 the future attractor is unphysical (CDM density becomes negative).…”

“…In order to extend earlier work in [42,43] and to explore a generalisation of previous work in [39] that considered DE as a cosmological constant, we studied recently [44] a dynamical systems analysis of an LTB interactive mixture of CDM (dust) and DE (fluid with p/ρ = w, w = const. < −1/3), under the assumption of an interaction driven by CDM: i.e.…”

“…• The CDM driven mixture examined in [44]: the phase space position of the past attractor (Big Bang) depended on the parameters α and w. For α > 0 (energy transfer from DE to CDM) the past attractor describes a well behaved CDM dominated scenario. However, for α < 0 (energy transfer from CDM to DE) the DE density became negative in phase space regions around the past attractor (irrespective of initial conditions), thus signalling an unphysical past evolution that is inconsistent with all observational data.…”