Apparent and average acceleration of the Universe

TL;DR

This paper investigates the relationship between volume deceleration parameters from averaging schemes and supernova observations, finding that realistic models do not support the idea that backreaction explains cosmic acceleration.

Contribution

It clarifies the connection between averaged deceleration parameters and observational data, challenging previous claims that backreaction could mimic dark energy.

Findings

Realistic Lemaître–Tolman models have positive volume deceleration parameter.

Models fitting supernova data do not show negative volume deceleration.

Unrealistic models can exhibit negative volume deceleration, but are not physically plausible.

Abstract

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