Non-Spherical Szekeres models in the language of Cosmological Perturbations

Abstract

We study the differences and equivalences between the non-perturbative description of the evolution of cosmic structure furnished by the Szekeres dust models (a non-spherical exact solution of Einstein's equations) and the dynamics of Cosmological Perturbation Theory (CPT) for dust sources in a $\Lambda$CDM background. We show how the dynamics of Szekeres models can be described by evolution equations given in terms of "exact fluctuations" that identically reduce (at all orders) to evolution equations of CPT in the comoving isochronous gauge. We explicitly show how Szekeres linearised exact fluctuations are specific (deterministic) realisations of standard linear perturbations of CPT given as random fields but, as opposed to the latter perturbations, they can be evolved exactly into the full non-linear regime. We prove two important results: (i) the conservation of the curvature perturbation (at all scales) also holds for the appropriate approximation of the exact Szekeres fluctuations in a $\Lambda$CDM background, and (ii) the different collapse morphologies of Szekeres models yields, at nonlinear order, different functional forms for the growth factor that follows from the study of redshift space distortions. The metric based potentials used in linear CPT are computed in terms of the parameters of the linearised Szekeres models, thus allowing us to relate our results to linear CPT results in other gauges. We believe that these results provide a solid starting stage to examine the role of non-perturbative General Relativity in current cosmological research.

V2: Minor comments and a couple of references added. Version accepted for publication in PRD

References in corpus (22)

• 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
• N-body methods for relativistic cosmology
• Linear kinetic Sunyaev-Zel'dovich effect and void models for acceleration
• Ellipsoidal halo finders and implications for models of triaxial halo formation
• Structure formation in the quasispherical Szekeres model
• Dark Energy or Apparent Acceleration Due to a Relativistic Cosmological Model More Complex than FLRW?
• Cosmic spherical void via coarse-graining and averaging non-spherical structures
• Redshift propagation equations in the ${\beta }^{\prime }\ne 0$ Szekeres models
• Probability of primordial black hole formation and its dependence on the radial profile of initial configurations
• Physical and Geometrical Interpretation of the epsilon <= 0 Szekeres Models
• Einstein's signature in cosmological large-scale structure
• Non-Gaussian corrections to the probability distribution of the curvature perturbation from inflation
• Exact nonlinear inhomogeneities in $\Lambda$CDM cosmology
• Volume averaging in the quasispherical Szekeres model
• Is the shell-focusing singularity of Szekeres space-time visible?
• On spherical dust fluctuations: the exact vs. the perturbative approach
• CMB dipoles and other low-order multipoles in the quasispherical Szekeres model
• Evolution of isolated overdensities as a control on cosmological N body simulations
• Modelling Inhomogeneity in Szekeres Spacetime
• A Relativistic view on large scale N-body simulations

Cited by in corpus (18)

• On average properties of inhomogeneous fluids in general relativity III: general fluid cosmologies
• Light propagation in Swiss cheese models of random close-packed Szekeres structures: Effects of anisotropy and comparisons with perturbative results
• Symmetry and Equivalence in Szekeres Models
• Lagrangian theory of structure formation in relativistic cosmology. VI. Comparison with Szekeres exact solutions
• Non-comoving Cold Dark Matter in a $\Lambda$CDM background
• Gauss-Bonnet-Chern approach to the averaged Universe
• Frame Rotation in the Szekeres Spacetimes
• Interactive mixture of inhomogeneous dark fluids driven by dark energy: a dynamical systems analysis
• Black hole formation from the gravitational collapse of a non-spherical network of structures
• Cyclic Szekeres Universes
• Consequences of using a smooth cosmic distance in a lumpy universe: I
• Non-comoving baryons and cold dark matter in cosmic voids
• Inhomogeneous spacetimes in Einstein-æther Cosmology
• Inhomogeneous spacetimes in Weyl integrable geometry with matter source
• Beyond relativistic Lagrangian perturbation theory. I. An exact-solution controlled model for structure formation
• Quasilocal horizons in inhomogeneous cosmological models
• An effective $\mathbf{\Lambda }$-Szekeres modelling of the local Universe with Cosmicflows-4
• Gravitational Entropy in Szekeres Class I Models