Inhomogeneities in the Universe with exact solutions of General
  Relativity
  It is commonly stated that we have entered the era of precision cosmology in
which a number of important observations have reached a degree of precision,
and a level of agreement with theory, that is comparable with many Earth-based
physics experiments. One of the consequences is the need to examine at what
point our usual, well-worn assumption of homogeneity associated to the use of
perturbation theory begins to compromise the accuracy of our models. It is now
a widely accepted fact that the effect of the inhomogeneities observed in the
Universe cannot be ignored when one wants to construct an accurate cosmological
model. Well-established physics can explain several of the observed phenomena
without introducing highly speculative elements, like dark matter, dark energy,
exponential expansion at densities never attained in any experiment (i.e.
inflation), and the like. Two main classes of methods are currently used to
deal with these issues. Averaging, sometimes linked to fitting procedures a la
Stoegger and Ellis, provide us with one promising way of solving the problem.
Another approach is the use of exact inhomogeneous solutions of General
Relativity. This will be developed here.
