The dark energy phenomenon from backreacation effect

In this paper, we interpret the dark energy phenomenon as an averaged effect caused by small scale inhomogeneities of the universe with the use of the spatial averaged approach of Buchert. Two models are considered here, one of which assumes that the backreaction term ${\cal Q}_\CD$ and the averaged spatial Ricci scalar $\average{\CR}$ obey the scaling laws of the volume scale factor $a_\CD$ at adequately late times, and the other one adopts the ansatz that the backreaction term ${\cal Q}_\CD$ is a constant in the recent universe. Thanks to the effective geometry introduced by Larena et. al. in their previous work, we confront these two backreaction models with latest type Ia supernova and Hubble parameter observations, coming out with the results that the constant backreaction model is slightly favoured over the other model, and within $1\sigma$ confidence interval of the parameter $n$ in the scaling backreaction model, $\mid{\cal Q}_\CD\mid$ decreases with the increase of the volume scale factor $a_\CD$ at adequately late times. Also, the numerical simulation results show that the constant backreaction model predicts a smaller expansion rate and decelerated expansion rate than the other model does at redshifts higher than about 1, and both backreaction terms begin to accelerate the universe at a redshift around 0.6. In addition, by confronting the standard cosmological model against the same datasets, we find that the effective geometry tends to push the constraint toward a smaller cosmological constant term.