Challenging dark energy with exact inhomogeneous models

Abstract
The dimming of the SN Ia apparent luminosity is generally ascribed to the influence of a “dark energy” component, which is supposed to yield a late-time acceleration of the Universe expansion rate. However, this interpretation assumes we are leaving in an homogeneous Universe where the influence of the inhomogeneities is negligible at all scales. Now, the last years have experienced an increase in the papers devoted to the study of such an influence and two main types of methods have been developed to deal with this problem: one is directed at evaluating backreaction effects with averaging strategies, the other makes use of models which are exact solutions of Einstein's equations and which, as they become more and more sophisticated, are able to reproduce the largest possible data sets (not only the supernovae). We focus here our interest on the later method and review the most achieved among the latest contributions available in the literature.