Tests and problems of the standard model in Cosmology
  The main foundations of the standard $\Lambda $CDM model of cosmology are
that: 1) The redshifts of the galaxies are due to the expansion of the Universe
plus peculiar motions; 2) The cosmic microwave background radiation and its
anisotropies derive from the high energy primordial Universe when matter and
radiation became decoupled; 3) The abundance pattern of the light elements is
explained in terms of primordial nucleosynthesis; and 4) The formation and
evolution of galaxies can be explained only in terms of gravitation within a
inflation+dark matter+dark energy scenario. Numerous tests have been carried
out on these ideas and, although the standard model works pretty well in
fitting many observations, there are also many data that present apparent
caveats to be understood with it. In this paper, I offer a review of these
tests and problems, as well as some examples of alternative models.
