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

Understand

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.