Imitating accelerated expansion of the Universe by matter inhomogeneities - corrections of some misunderstandings

Abstract

A number of misunderstandings about modeling the apparent accelerated expansion of the Universe, and about the `weak singularity' are clarified: 1. Of the five definitions of the deceleration parameter given by Hirata and Seljak (HS), only $q_1$ is a correct invariant measure of acceleration/deceleration of expansion. The $q_3$ and $q_4$ are unrelated to acceleration in an inhomogeneous model. 2. The averaging over directions involved in the definition of $q_4$ does not correspond to what is done in observational astronomy. 3. HS's equation (38) connecting $q_4$ to the flow invariants gives self-contradictory results when applied at the centre of symmetry of the Lema\^ıtre-Tolman (L-T) model. The intermediate equation (31) that determines $q_{3^{\prime }}$ is correct, but approximate, so it cannot be used for determining the sign of the deceleration parameter. Even so, at the centre of symmetry of the L-T model, it puts no limitation on the sign of $q_{3^{\prime }}(0)$. 4. The `weak singularity' of Vanderveld {\it et al.} is a conical profile of mass density at the centre - a perfectly acceptable configuration. 5. The so-called `critical point' in the equations of the `inverse problem' for a central observer in an L-T model is a manifestation of the apparent horizon - a common property of the past light cones in zero-lambda L-T models, perfectly manageable if the equations are correctly integrated.

15 pages. Completely rewritten to match the published version. We added discussion of 2 key papers cited by VFW and identified more clearly the assumptions, approximations and mistakes that led to certain misconceptions.

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Cited by in corpus (35)

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• Inhomogeneous cosmological models: exact solutions and their applications
• Establishing homogeneity of the universe in the shadow of dark energy
• Observational constraints on inhomogeneous cosmological models without dark energy
• Inhomogeneity effects in Cosmology
• Emerging spatial curvature can resolve the tension between high-redshift CMB and low-redshift distance ladder measurements of the Hubble constant
• The Cosmic Microwave Background in an Inhomogeneous Universe - why void models of dark energy are only weakly constrained by the CMB
• Is backreaction really small within concordance cosmology?
• Ricci focusing, shearing, and the expansion rate in an almost homogeneous Universe
• Inhomogeneous cosmology and backreaction: Current status and future prospects
• Measurement of marked correlation functions in SDSS-III Baryon Oscillation Spectroscopic Survey using LOWZ galaxies in Data Release 12
• Thermodynamics of the Variable Modified Chaplygin gas
• Redshift drift in a pressure-gradient cosmology
• Observational Constraints on the Averaged Universe
• Some clarifications about Lemaître-Tolman models of the Universe used to deal with the dark energy problem
• Accelerating expansion or inhomogeneity? A comparison of the $\Lambda$CDM and Lema\^ıtre - Tolman models
• Hyperbolically symmetric versions of Lemaitre-Tolman-Bondi spacetimes
• Spherically symmetric inhomogeneous model with Chaplygin gas
• A critical assessment of some inhomogeneous pressure Stephani models
• FRW type of cosmology with a Chaplygin gas
• All black holes in Lemaitre-Tolman-Bondi inhomogeneous dust collapse
• Visualizing Spacetime Curvature via Gradient Flows I: Introduction
• Inhomogeneities in dusty universe - a possible alternative to dark energy?
• Constraining Modified Chaplygin gas parameters
• Exact inhomogeneous models and the drift of light rays induced by nonsymmetric flow of the cosmic medium
• Kullback-Leibler entropy and Penrose conjecture in the Lemaitre-Tolman-Bondi model
• Inverse Construction of the $\Lambda$LTB Model from a Distance-redshift Relation
• Mimicking acceleration in the constant-bang-time Lema\^ıtre -- Tolman model: Shell crossings, density distributions and light cones
• Thermodynamic perfect fluid spheres admitting an orthogonal flat synchronization
• Properties of blueshifted light rays in quasispherical Szekeres metrics
• Local Peculiar Motions in McVittie and LTB Spacetimes
• How large is the contribution of cosmic web to ${\Omega }_{\Lambda }$ ? A preliminary study on a novel inhomogenous model
• An Alternative Approach to the Exact Solution of FRW-Type Spacetime with a Generalized Chaplygin Gas
• Central density cusps in the Lemaître-Tolman solutions
• Emergent Universe Scenario in the Modified Chaplygin gas : Towards an Exact Solution and Observational Constraints