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In order to explain the current acceleration of the Universe, the fine tuningproblem of the cosmological constant $\Lambda$ and the cosmic coincidenceproblem, different alternative models have been proposed in the literature. Weuse the most recent observational data from CMB (Planck 2018 final datarelease) and LSS (SDSS, WiggleZ, VIPERS) to constrain dynamical dark energy(DE) models. The CMB shift parameter, which traditionally has been used todetermine the main cosmological parameters of the standard model $\Lambda CDM$is employed in addition to data from redshift-space distortions through thegrowth 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 cosmologicalexpansion and the main properties of DE. From the evolution of $q(z)$ we founda slowdown of acceleration behaviour at low redshifts, and by using the Akaikeand Bayesian Information Criterion (AIC, BIC) we discriminate different modelsthose that are better suited to the observational data, finding that theinteractive dark energy (IDE) model is the most favoured by observational data,including information from SNIa and Hz. The analysis shows that the IDE modelis followed closely by EDE and $\Lambda CDM$ models, which in some cases fitbetter the observational data with individual probes.

Exploring the Dark Universe: constraints on dynamical Dark Energy models from CMB, BAO and growth rate measurements