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 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.
