Development of a model to investigate the effect of the bias in SNIa measurements related to the inhomogeneity of space

Abstract

It has been suggested recently that the appparent accelerated expansion of the universe could be explained by a bias in the SNIa measurements. Such events indeed occur mainly in overdense regions, where matter is located, and whose dynamics can perhaps not been considered as representative of the one of the universe. In this article, we develop a model to investigate in more detail the effect of this bias. This model depends on one single parameter, related to the void fraction of space, and leads to simple analytical relations. We in particular determine the average metric tensor in overdense regions, and deduce that the scale factor and the rate at which time progresses in such regions differ significantly from the corresponding values expected on the average space. We then quantitatively deduce how redshift and luminosity distance measurements are affected by the bias, taking into account the perturbation of the metric tensor. Using a value for the void fraction corresponding to the order of magnitude found in the literature, we show that the model is able to predict a distance modulus versus redshift relation being in excellent aggreement with the one corresponding to a universe characterized by $\Omega_{m,0} = 0.3$ and $\Omega_{\Lambda,0} = 0.7$.