Weighed scalar averaging in LTB dust models, part I: statistical fluctuations and gravitational entropy

Abstract

We introduce a weighed scalar average formalism ("q-average") for the study of the theoretical properties and the dynamics of spherically symmetric Lemaitre-Tolman-Bondi (LTB) dust models models. The "q-scalars" that emerge by applying the q-averages to the density, Hubble expansion and spatial curvature (which are common to FLRW models) are directly expressible in terms of curvature and kinematic invariants and identically satisfy FLRW evolution laws without the back-reaction terms that characterize Buchert's average. The local and non-local fluctuations and perturbations with respect to the q-average convey the effects of inhomogeneity through the ratio of curvature and kinematic invariants and the magnitude of radial gradients. All curvature and kinematic proper tensors that characterize the models are expressible as irreducible algebraic expansions on the metric and 4-velocity, whose coefficients are the q-scalars and their linear and quadratic local fluctuations. All invariant contractions of these tensors are quadratic fluctuations, whose q-averages are directly and exactly related to statistical correlation moments of the density and Hubble expansion scalar. We explore the application of this formalism to a definition of a gravitational entropy functional proposed by Hosoya et al (2004 Phys. Rev. Lett. 92 141302). We show that a positive entropy production follows from a negative correlation between fluctuations of the density and Hubble scalar, providing a brief outline on its fulfillment in various LTB models and regions. While the q-average formalism is specially suited for LTB and Szekeres models, it may provide a valuable theoretical insight on the properties of scalar averaging in inhomogeneous spacetimes in general.

27 pages in IOP format, 1 figure. Matches version accepted for publication in Classical and Quantum Gravity

References in corpus (26)

• Lemaitre-Tolman-Bondi model and accelerating expansion
• The universe seen at different scales
• On cosmological observables in a swiss-cheese universe
• CMB anisotropies seen by an off-center observer in a spherically symmetric inhomogeneous universe
• Correspondence between kinematical backreaction and scalar field cosmologies - the `morphon field'
• 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
• Lemaitre-Tolman-Bondi collapse from the perspective of loop quantum gravity
• The influence of structure formation on the cosmic expansion
• Information Entropy in Cosmology
• A cosmic equation of state for the inhomogeneous Universe: can a global far-from-equilibrium state explain Dark Energy?
• The Spatial Averaging Limit of Covariant Macroscopic Gravity - Scalar Corrections to the Cosmological Equations
• Averaging in Spherically Symmetric Cosmology
• Cosmic Inhomogeneities and the Average Cosmological Dynamics
• 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
• Large-scale growth evolution in the Szekeres inhomogeneous cosmological models with comparison to growth data
• A dynamical system approach to inhomogeneous dust solutions
• A Covariant Road to Spatial Averaging in Cosmology : Scalar Corrections to the Cosmological Equations
• Relative information entropy of an inhomogeneous universe

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• Gauss-Bonnet-Chern approach to the averaged Universe
• Thermodynamics and Lemaitre-Tolman-Bondi void models
• Interactive mixture of inhomogeneous dark fluids driven by dark energy: a dynamical systems analysis
• How appropriate are the gravitational entropy proposals for traversable wormholes?
• Non-comoving baryons and cold dark matter in cosmic voids
• Kullback-Leibler entropy and Penrose conjecture in the Lemaitre-Tolman-Bondi model
• An investigation on gravitational entropy of cosmological models
• Arrow of time and gravitational entropy in collapse
• Gravitational entropy of cosmic expansion
• Evolution equations dynamical system of the Lemaître--Tolman--Bondi metric containing coupled dark energy
• Weyl Curvature Hypothesis in light of Quantum Backreaction at Cosmological Singularities or Bounces
• Ricci Time in the Lemaitre-Tolman Model and the Block Universe