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

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 LemaItre-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 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 (AH)-a common property of the past light cones in zero-lambda L-T models, perfectly manageable if the equations are correctly integrated.