Evolution of radial profiles in regular Lemaître–Tolman–Bondi dust models

Abstract

We undertake a comprehensive and rigorous analytic study of the evolution of radial profiles of covariant scalars in regular Lemaître–Tolman–Bondi (LTB) dust models. We consider specifically the phenomenon of ‘profile inversions’ in which an initial clump profile of density, spatial curvature or the expansion scalar might evolve into a void profile (and vice versa). Previous work in the literature on models with density void profiles and/or allowing for density profile inversions is given full generalization, with some erroneous results corrected. We prove rigorously that if an evolution without shell crossings is assumed, then only the ‘clump to void’ inversion can occur in density profiles, and only in hyperbolic models or regions with negative spatial curvature. The profiles of spatial curvature follow similar patterns as those of the density, with ‘clump to void’ inversions only possible for hyperbolic models or regions. However, profiles of the expansion scalar are less restrictive, with profile inversions necessarily taking place in elliptic models. We also examine radial profiles in special LTB configurations: closed elliptic models, models with a simultaneous big bang singularity, as well as a locally collapsing elliptic region surrounded by an expanding hyperbolic background. The general analytic statements that we obtain allow for setting up the right initial conditions to construct fully regular LTB models with any specific qualitative requirements for the profiles of all scalars and their time evolution. The results presented can be very useful in guiding future numerical work on these models and in revising previous analytic work on all their applications.

Effects of inhomogeneities on apparent cosmological observables: “fake” evolving dark energy

“…Since all the models considered here describe compensated inhomogeneities, they show both phantom and quiescence behaviors, but we can see that the sign of the variation of The relation between density profiles and the free parameters of the LTB metric is quite difficult and elaborate, as shown for example in [38,40]. One useful way to analyze the relation between the profile of k(r) with that of ρ(r) is to consider the linear theory limit.…”

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

“…In general, the evolution of the models needs to be determined numerically. If = 0 we have a shell crossing singularity, which means that initial conditions should be found to avoid this happening (it is not possible to provide simple guidelines for this, as in dust solutions with zero cosmological constant, see [29][30][31]34]). As shown in previous work (for example [44]) the qscalar formalism fails at shell crossing singularities because the fluctuations δ m , δ e , δ H diverge.…”

“…These solutions have been extensively studied (with zero and nonzero cosmological constant) and used in a wide range of astrophysical and cosmological modelling (see extensive reviews in [29][30][31][32]). In particular, a better understanding of their theoretical properties follows by describing their dynamics in terms of "quasi-local scalars" [33][34][35][36] (to be denoted henceforth as "q-scalars"), which are related to averages of standard covariant scalars and satisfy FLRW dynamical equations and scaling laws [35].…”

Relativistic cosmology number densities in void-Lemaître-Tolman-Bondi models

“…Sollerman et al 2009), some of them cannot be ruled out entirely yet. Among these models, motivated mainly as alternative to dark energy, various non-homogeneous cosmologies have been proposed, with an increasing interest in the past few years (Hellaby & Alfedeel 2009;Alfedeel & Hellaby 2010;February et al 2010;Biswas et al 2010;Sussman 2010;Bolejko et al 2011b;Nadathur & Sarkar 2011;Clarkson & Regis 2011;Clarkson et al 2012;Regis & Clarkson 2012;Meures & Bruni 2012;Humphreys et al 2012;Nishikawa et al 2012;Valkenburg et al 2014;Wang & Zhang 2012;Hellaby 2012;Hoyle et al 2013;de Putter et al 2012;Keenan et al 2012;Fleury et al 2013). Some recent reviews include Célérier (2007), Bolejko et al (2011a), Ellis (2011), and Krasiński (2014).…”