A dynamical system study of the inhomogeneous Λ-CDM model

Abstract

PACS numbers: 98.80.-k, 04.20.-q, 95.36.+x, 95.35.+d Introduction.From a phenomenological and empiric point of view, cosmological observations are usually tested as a first attempt by fitting them to the so-called Λ-CDM model, which is a FLRW spacetime with flat spacelike sections, whose source is dust (cold dark matter CDM) and a Λ field (dark energy) (see [1,2] for comprehensive reviews). Although the universe may be nearly homogeneous at scales larger than the so-called homogeneity scale (over 150-300 Mpc), thus justifying the use of linear perturbations in its dynamical study, it is clearly inhomogeneous at smaller scales in which structure formation mostly involving CDM has taken place. Hence, the study of inhomogeneous sources made of dust and a nonzero "Λ field" is a very relevant topic. In particular, spacetimes of this type of source with spherical symmetry provide simple but nontrivial inhomogeneous generalizations of the Λ-CDM model.

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

“…We shall follow the methodology described in [15,18,19], which we will summarize briefly in order to clarify the notation used in this work. We consider spherically symmetric space-times whose source is an anisotropic fluid…”

“…In particular, the spherically symmetric Lemaître-Tolman-Bondi (LTB) metric QuasiLocal (QL) scalar approach [15] can be used to study a local spherical exact solution that matches the homogeneous FLRW at larger scales and the linear perturbations of the FLRW metric can be related to the LTB fluctuations with respect to the QL scalars defined [16]. LTB metrics are well known in the context of pure dust solutions (see [17] for a review), and also in the context of dust plus a cosmological constant [18,16], but not much work is done in the context of more exotic sources such as DE or CDE [19]. In this sense, we believe that an understanding of the dynamics of the inhomogeneous metrics containing those sources is necessary.…”

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

“…ξ (the appropriate integrability conditions are discussed in detail in [39]). Taking this into account, the LTB metric functions follow from evaluat-…”

“…The q-scalars and their fluctuations allow for a consistent dynamical systems study of the models (with zero cosmological constant in [37,38] and nonzero in [39]). An important theoretical connection with cosmological perturbation theory follows from the fact that the fluctuations of the q-scalars provide an exact analytic (and covariant) generalisation of gauge invariant cosmological perturbations in the isochronous gauge [38,40].…”

“…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.…”