Apparent and average accelerations of the Universe

In this paper we consider the relation between the volume deceleration parameter obtained within the Buchert averaging scheme and the deceleration parameter derived from supernova observation. This work was motivated by recent findings that showed that there are models which despite having Λ = 0 have volume deceleration parameter qvol < 0. This opens the possibility that back-reaction and averaging effects may be used as an interesting alternative explanation to the dark energy phenomenon. We have calculated qvol in some Lemâıtre–Tolman models. For those models which are chosen to be realistic and which fit the supernova data, we find that qvol > 0, while those models which we have been able to find which exhibit qvol < 0 turn out to be unrealistic. This indicates that care must be exercised in relating the deceleration parameter to observations.