Effects of inhomogeneities on the expansion of the Universe: a challenge to dark energy?

The current standard model of cosmology, the LambdaCDM model, is based on the homogeneous FLRW solutions of the Einstein equations to which some perturbations are added to account for the CMB features and structure formation at large scales. This model fits rather well the observations provided 95% of the energy density budget of the Universe should be of an unknown physical nature, i.e. dark matter and dark energy. Now, the aim of a cosmological model is not merely to reproduce the observations, but also to give a physical understanding of the Universe we live in. Moreover, even if the assumption of homogeneity seems to be more or less valid at large scales, it appears to be in contradiction with observations at intermediate scales (between the scale of non linear structure formation and that where structures virialize). This is the reason why, during the last decade, a community of researchers formed whose aim was to look for the best way to take into account the influence of the inhomogeneities seen in the Universe and to construct accurate cosmological models which could possibly get rid of the dark components. This task, which is still in its infancy, is currently progressing towards promising results. Two types of methods can be found in the literature: spatial averaging of scalar quantities and use of exact inhomogeneous solutions of General Relativity. We will give here a brief report of the second one.