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

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

2009-03-24

arxiv.org/abs/0903.4070v2

Gen.Rel.Grav.42:2453-2475,2010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages. Completely rewritten to match the published version. We added discussion of 2 key papers cited by VFW and identified

Scientific paper

10.1007/s10714-010-0993-5

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\^{\i}tre-Tolman (L-T) model. The intermediate equation (31) that determines $q_{3'}$ 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 $q_{3'}(0)$. 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.

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