Interacting dark energy models in Cosmology and large-scale structure
  observational tests
  Modern Cosmology offers us a great understanding of the universe with
striking precision, made possible by the modern technologies of the newest
generations of telescopes. The standard cosmological model, however, is not
absent of theoretical problems and open questions. One possibility that has
been put forward is the existence of a coupling between dark sectors. The idea
of an interaction between the dark components could help physicists understand
why we live in an epoch of the universe where dark matter and dark energy are
comparable in terms of energy density, which can be regarded as a coincidence
given that their time evolutions are completely different.
  We introduce the interaction phenomenologically and proceed to test models of
interaction with observations of redshift-space distortions. In a flat universe
composed only of those two fluids, we consider separately two forms of
interaction, through terms proportional to the densities of both dark energy
and dark matter. An analytic expression for the growth rate approximated as $f
= \Omega_{\mathrm{DM}}^{\gamma}$, where $\Omega_{\mathrm{DM}}$ is the
percentage contribution from the dark matter to the content of the universe and
$\gamma$ is the growth index, is derived in terms of the interaction strength
and of other parameters of the model in the first case, while for the second
model we show that a non-zero interaction cannot be accommodated by the index
growth approximation. The successful expressions obtained are then used to
compare the predictions with growth of structure observational data in a MCMC
code.
  We also employ observations of galaxy clusters to assess their virial state
via the modified Layzer-Irvine equation in order to detect signs of an
interaction, obtaining measurements of observed virial ratios, interaction
strength, rest virial ratio and departure from equilibrium for a set of
clusters. [abridged]
