Exploring the Dark Universe: constraints on dynamical Dark Energy models
  from CMB, BAO and growth rate measurements
  In order to explain the current acceleration of the Universe, the fine tuning
problem of the cosmological constant $\Lambda$ and the cosmic coincidence
problem, different alternative models have been proposed in the literature. We
use the most recent observational data from CMB (Planck 2018 final data
release) and LSS (SDSS, WiggleZ, VIPERS) to constrain dynamical dark energy
(DE) models. The CMB shift parameter, which traditionally has been used to
determine the main cosmological parameters of the standard model $\Lambda CDM$
is employed in addition to data from redshift-space distortions through the
growth parameter $A(z)=f(z)\sigma_{8}(z)$ to constrain the mass variance
$\sigma_{8}$. BAO data is also used to study the history of the cosmological
expansion and the main properties of DE. From the evolution of $q(z)$ we found
a slowdown of acceleration behaviour at low redshifts, and by using the Akaike
and Bayesian Information Criterion (AIC, BIC) we discriminate different models
those that are better suited to the observational data, finding that the
interactive dark energy (IDE) model is the most favoured by observational data,
including information from SNIa and Hz. The analysis shows that the IDE model
is followed closely by EDE and $\Lambda CDM$ models, which in some cases fit
better the observational data with individual probes.
