Multiple non-spherical structures from the extrema of Szekeres scalars

Abstract

We examine the spatial extrema (local maxima, minima and saddle points) of the covariant scalars (density, Hubble expansion, spatial curvature and eigenvalues of the shear and electric Weyl tensors) of the quasi-spherical Szekeres dust models. Sufficient conditions are obtained for the existence of distributions of multiple extrema in spatial comoving locations that can be prescribed through initial conditions. These distributions evolve without shell crossing singularities at least for ever expanding models (with or without cosmological constant) in the full evolution range where the models are valid. By considering the local maxima and minima of the density, our results allow for setting up elaborated networks of "pancake" shaped evolving cold dark matter over-densities and density voids whose spatial distribution and amplitudes can be controlled from initial data compatible with standard early Universe initial conditions. We believe that these results have an enormous range of potential application by providing a fully relativistic non-perturbative coarse grained modelling of cosmic structure at all scales.

Matches published version. 28 pages, 9 figures. Minor but important corrections were incorporated

References in corpus (25)

• The Laniakea supercluster of galaxies
• Full-Sky Weak Lensing Simulation with 70 Billion Particles
• What is dust? - Physical foundations of the averaging problem in cosmology
• Testing the Void against Cosmological data: fitting CMB, BAO, SN and H0
• Szekeres Swiss-Cheese model and supernova observations
• The Szekeres Swiss Cheese model and the CMB observations
• Linear kinetic Sunyaev-Zel'dovich effect and void models for acceleration
• Lagrangian theory of structure formation in relativistic cosmology I: Lagrangian framework and definition of a nonperturbative approximation
• Structure formation in the quasispherical Szekeres model
• Cosmic spherical void via coarse-graining and averaging non-spherical structures
• Dark Energy or Apparent Acceleration Due to a Relativistic Cosmological Model More Complex than FLRW?
• Redshift propagation equations in the ${\beta }^{\prime }\ne 0$ Szekeres models
• Probing spatial homogeneity with LTB models: a detailed discussion
• Exact nonlinear inhomogeneities in $\Lambda$CDM cosmology
• Lagrangian theory of structure formation in relativistic cosmology III: gravitoelectric perturbation and solution schemes at any order
• Methods for studying the accuracy of light propagation in N-body simulations
• Studying the precision of ray tracing techniques with Szekeres models
• Is the shell-focusing singularity of Szekeres space-time visible?
• The Great Attractor and the Shapley Concentration
• On spherical dust fluctuations: the exact vs. the perturbative approach
• CMB dipoles and other low-order multipoles in the quasispherical Szekeres model
• Modelling Inhomogeneity in Szekeres Spacetime
• Testing Dark Matter Clustering with Redshift Space Distortions
• A Relativistic view on large scale N-body simulations
• Can a void mimic the $\Lambda$ in $\Lambda$CDM?

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• Studying the precision of ray tracing techniques with Szekeres models
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• Non-Spherical Szekeres models in the language of Cosmological Perturbations
• Cosmological backreaction within the Szekeres model and emergence of spatial curvature
• Symmetry and Equivalence in Szekeres Models
• Gravitational entropy and the cosmological no-hair conjecture
• Lagrangian theory of structure formation in relativistic cosmology. VI. Comparison with Szekeres exact solutions
• Non-comoving Cold Dark Matter in a $\Lambda$CDM background
• Frame Rotation in the Szekeres Spacetimes
• Black hole formation from the gravitational collapse of a non-spherical network of structures
• Interactive mixture of inhomogeneous dark fluids driven by dark energy: a dynamical systems analysis
• Szekeres models: a covariant approach
• Physical geometry of the quasispherical Szekeres models
• Pancakes as opposed to Swiss Cheese
• Non-comoving baryons and cold dark matter in cosmic voids
• On general-relativistic Lagrangian perturbation theory and its non-perturbative generalization
• Beyond relativistic Lagrangian perturbation theory. I. An exact-solution controlled model for structure formation
• Properties of blueshifted light rays in quasispherical Szekeres metrics
• Quasilocal horizons in inhomogeneous cosmological models
• Rotation, Embedding and Topology for the Szekeres Geometry
• Gravitational Entropy in Szekeres Class I Models
• An effective $\mathbf{\Lambda }$-Szekeres modelling of the local Universe with Cosmicflows-4