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.
