Back-reaction and effective acceleration in generic LTB dust models

Abstract

We provide a thorough examination of the conditions for the existence of back-reaction and an "effective" acceleration (in the context of Buchert's averaging formalism) in regular generic spherically symmetric Lemaitre-Tolman-Bondi (LTB) dust models. By considering arbitrary spherical comoving domains, we verify rigorously the fulfillment of these conditions expressed in terms of suitable scalar variables that are evaluated at the boundary of every domain. Effective deceleration necessarily occurs in all domains in: (a) the asymptotic radial range of models converging to a FLRW background, (b) the asymptotic time range of non-vacuum hyperbolic models, (c) LTB self-similar solutions and (d) near a simultaneous big bang. Accelerating domains are proven to exist in the following scenarios: (i) central vacuum regions, (ii) central (non-vacuum) density voids, (iii) the intermediate radial range of models converging to a FLRW background, (iv) the asymptotic radial range of models converging to a Minkowski vacuum and (v) domains near and/or intersecting a non-simultaneous big bang. All these scenarios occur in hyperbolic models with negative averaged and local spatial curvature, though scenarios (iv) and (v) are also possible in low density regions of a class of elliptic models in which local spatial curvature is negative but its average is positive. Rough numerical estimates between -0.003 and -0.5 were found for the effective deceleration parameter. While the existence of accelerating domains cannot be ruled out in models converging to an Einstein de Sitter background and in domains undergoing gravitational collapse, the conditions for this are very restrictive. The results obtained may provide important theoretical clues on the effects of back-reaction and averaging in more general non-spherical models.

Final version accepted for publication in Classical and Quantum Gravity. 47 pages in IOP LaTeX macros, 12 pdf figures

References in corpus (37)

• Cosmic clocks, cosmic variance and cosmic averages
• Does the growth of structure affect our dynamical models of the universe? The averaging, backreaction and fitting problems in cosmology
• Lemaitre-Tolman-Bondi model and accelerating expansion
• The universe seen at different scales
• On cosmological observables in a swiss-cheese universe
• A new framework for analyzing the effects of small scale inhomogeneities in cosmology
• CMB anisotropies seen by an off-center observer in a spherically symmetric inhomogeneous universe
• Inhomogeneity and the foundations of concordance cosmology
• What is dust? - Physical foundations of the averaging problem in cosmology
• Correspondence between kinematical backreaction and scalar field cosmologies - the `morphon field'
• Can we avoid dark energy?
• Light-cone averages in a swiss-cheese universe
• Scalar Perturbations on Lemaitre-Tolman-Bondi Spacetimes
• The supernova Hubble diagram for off-center observers in a spherically symmetric inhomogeneous universe
• Multiscale cosmology and structure-emerging Dark Energy: A plausibility analysis
• Constraints on backreaction in dust universes
• Can inhomogeneties accelerate the cosmic volume expansion?
• The Possibility of Cosmic Acceleration via Spatial Averaging in Lemaitre-Tolman-Bondi Models
• On the curvature of the present-day Universe
• Applicability of the linearly perturbed FRW metric and Newtonian cosmology
• Gravitational energy as dark energy: Concordance of cosmological tests
• A cosmic equation of state for the inhomogeneous Universe: can a global far-from-equilibrium state explain Dark Energy?
• A novel approach to the dynamics of Szekeres dust models
• The Spatial Averaging Limit of Covariant Macroscopic Gravity - Scalar Corrections to the Cosmological Equations
• Cosmic spherical void via coarse-graining and averaging non-spherical structures
• Averaging in Spherically Symmetric Cosmology
• Description of our cosmological spacetime as a perturbed conformal Newtonian metric and implications for the backreaction proposal for the accelerating universe
• Cosmic Inhomogeneities and the Average Cosmological Dynamics
• Accelerated expansion without dark energy
• Cosmological acceleration from structure formation
• Explicit Cosmological Coarse Graining via Spatial Averaging
• A Markov Chain Monte Carlo approach to the study of massive black hole binary systems with LISA
• Backreaction of Cosmological Perturbations in Covariant Macroscopic Gravity
• Evolution of radial profiles in regular Lemaitre-Tolman-Bondi dust models
• On the role of shear in cosmological averaging II: large voids, non-empty voids and a network of different voids
• A Covariant Road to Spatial Averaging in Cosmology : Scalar Corrections to the Cosmological Equations
• A new approach for doing theoretical and numeric work with Lemaitre-Tolman-Bondi dust models

Cited by in corpus (38)

• Establishing homogeneity of the universe in the shadow of dark energy
• Observational constraints on inhomogeneous cosmological models without dark energy
• Average expansion rate and light propagation in a cosmological Tardis spacetime
• Lagrangian theory of structure formation in relativistic cosmology II: average properties of a generic evolution model
• A novel approach to the dynamics of Szekeres dust models
• On average properties of inhomogeneous fluids in general relativity III: general fluid cosmologies
• Ricci focusing, shearing, and the expansion rate in an almost homogeneous Universe
• Local and non-local measures of acceleration in cosmology
• Swiss-cheese models and the Dyer-Roeder approximation
• The growth of structure in the Szekeres inhomogeneous cosmological models and the matter-dominated era
• Exact spherically-symmetric inhomogeneous model with n perfect fluids
• Perceiving the equation of state of Dark Energy while living in a Cold Spot
• Inhomogeneous cosmology and backreaction: Current status and future prospects
• Light propagation in inhomogeneous and anisotropic cosmologies
• Backreaction in Cosmology
• Gravitational entropies in LTB dust models
• Large-scale growth evolution in the Szekeres inhomogeneous cosmological models with comparison to growth data
• Invariant characterization of the growing and decaying density modes in LTB dust models
• Effect of inhomogeneities on high precision measurements of cosmological distances
• A solution of the dark energy and its coincidence problem based on local antigravity sources without fine-tuning or new scales
• On spherical dust fluctuations: the exact vs. the perturbative approach
• Hyperbolically symmetric versions of Lemaitre-Tolman-Bondi spacetimes
• On the covariance of scalar averaging and backreaction in relativistic inhomogeneous cosmology
• Relativistic cosmological perturbation scheme on a general background: scalar perturbations for irrotational dust
• Cosmic bulk viscosity through backreaction
• Gauss-Bonnet-Chern approach to the averaged Universe
• Averaged Lemaître-Tolman-Bondi dynamics
• Lightcone Averaging and Precision Cosmology
• Exact inhomogeneous models and the drift of light rays induced by nonsymmetric flow of the cosmic medium
• Expansion and Growth of Structure Observables in a Macroscopic Gravity Averaged Universe
• Kullback-Leibler entropy and Penrose conjecture in the Lemaitre-Tolman-Bondi model
• Unified description of galactic dynamics and the cosmological constant
• Beyond relativistic Lagrangian perturbation theory. I. An exact-solution controlled model for structure formation
• Averaging in LRS class II spacetimes
• Constraining the swiss-cheese IR-fixed point cosmology with cosmic expansion
• Coupled Dark Energy field variation
• The effect of cosmic inhomogeneities on the average cosmological dynamics
• The averaging problem on the past null cone in inhomogeneous dust cosmologies