Models of voids in elliptic universes

Chamorro, A.

doi:10.1086/170761

Cited by 7 publications

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“…These shells can be considered as some sort of "topological" density clumps or voids (the same remark applies to spatial curvature or the expansion scalar), and are a product of the spherical S 3 topology of the rest frames 3 T [t], and as such are not related to a profile inversion produced by the evolution of the models given generic initial conditions (as is the case for the TV's that were examined in sections 3-8). As a consequence, models of topological clumps/void profiles [29,30] are rather artificial constructions.…”

Section: Final Discussionmentioning

confidence: 99%

“…However, as in the case of a single TV of R, these regions are concentric under-dense or over-dense thick spherical shells, not compact regions, and are fixed features (not evolving "density waves") that follow from the choice of an initial 3 T [t i ] in which initial value functions R i , m qi , k qi have an arbitrary number of common TV's. This inherent feature of closed elliptic models to produce TV's of density has been used in the literature to generate void models by means of compound configurations constructed by suitably matching regions of closed elliptic models and sections of FLRW dust models [29,30]. Since the voids and clumps in these configurations do not follow from generic initial conditions, they are wholly artificial and will not be considered any further.…”

Section: Profiles Of the Expansion Scalarmentioning

confidence: 99%

“…Some authors [27,28] have examined non-perturbative void profiles numerically in the context of structure formation scenarios (though, from our results in section 6, the elliptic models in [27] cannot be free from shell crossings). In some suggested configurations the void is modeled as an under-dense FLRW region, which is connected to a cosmic "background" through a section of a closed elliptic model [29,30]. In other articles [31,32,33], the void is an LTB region containing a center, matched at a fixed comoving radius to another LTB region (the "envelope"), which in turn is matched to a FLRW "exterior".…”

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Evolution of radial profiles in regular Lemaitre-Tolman-Bondi dust models

Sussman

2010

Preprint

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We undertake a comprehensive and rigorous analytic study of the evolution of radial profiles of covariant scalars in regular Lemaître-Tolman-Bondi 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.

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Section: Final Discussionmentioning

confidence: 99%

Section: Profiles Of the Expansion Scalarmentioning

confidence: 99%

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confidence: 99%

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Evolution of radial profiles in regular Lemaitre-Tolman-Bondi dust models

Sussman

2010

Preprint

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“…Although most treatments of void evolution have been within a Newtonian framework, attempts to model voids within a fully general-relativistic framework have also been undertaken [358,495,357,496,332,453,454,416,71,108]; the study of voids has been extended to include models with a cosmological constant [367].…”

Section: Void Expansionmentioning

confidence: 99%

Approximation methods for non-linear gravitational clustering

1995

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We discuss various analytical approximation methods for following the evolution of cosmological density perturbations into the strong (i.e. nonlinear) clustering regime. We start by giving a thorough treatment of linear gravitational instability in cosmological models and discussing the statistics of primordial density fluctuations produced in various scenarios of structure formation, and the role of non-baryonic dark matter. We critically review various methods for dealing with the non-linear evolution of density inhomogeneities, in the context of theories of the formation of galaxies and large-scale structure. These methods can be classified into five types: (i) simple extrapolations from linear theory, such as the high-peak model and the lognormal model; (ii) dynamical approximations, including the Zel'dovich approximation and its extensions; (iii) non-linear models based on purely geometric considerations, of which the main example is the Voronoi model; (iv) statistical solutions involving scaling arguments, such as the hierarchical closure ansatz for BBGKY, fractal models and the thermodynamic model of Saslaw; (v) numerical techniques based on particles and/or hydrodynamics. We compare the results of full dynamical evolution using particle codes and the various other approximation schemes. To put the models we discuss into perspective, we give a brief review of the observed properties of galaxy clustering and the statistical methods used to quantify it, such as correlation functions, power spectra, topology and spanning trees.

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“…Some authors [27,28] have examined non-perturbative void profiles numerically in the context of structure formation scenarios (though, from our results in section 6, the elliptic models in [27] cannot be free from shell crossings). In some suggested configurations the void is modeled as an under-dense FLRW region, which is connected to a cosmic 'background' through a section of a closed elliptic model [29,30]. In other articles [31][32][33], the void is an LTB region containing a center, matched at a fixed comoving radius to another LTB region (the 'envelope'), which in turn is matched to a FLRW 'exterior'.…”

Section: Introductionmentioning

confidence: 99%

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

Sussman¹

2010

Class. Quantum Grav.

123

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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.

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Models of voids in elliptic universes

Cited by 7 publications

References 0 publications

Evolution of radial profiles in regular Lemaitre-Tolman-Bondi dust models

Evolution of radial profiles in regular Lemaitre-Tolman-Bondi dust models

Approximation methods for non-linear gravitational clustering

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

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