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

الأصل · EN

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 q₁ is a correct invariant measure of acceleration/deceleration of expansion. The q₃ and q₄ are unrelated to acceleration in an inhomogeneous model. 2. The averaging over directions involved in the definition of q₄ does not correspond to what is done in observational astronomy. 3. HS's equation (38) connecting q₄ to the flow invariants gives self-contradictory results when applied at the centre of symmetry of the Lematre-Tolman (L-T) model. The intermediate equation (31) that determines q₃' 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 q₃'(0). 4. The `weak singularity' of Vanderveld 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.