Dynamical dark energy after Planck CMB final release and $H_0$ tension
  In this article we compare a variety of well known dynamical dark energy
models using the cosmic microwave background measurements from the 2018 Planck
legacy and 2015 Planck data releases, the baryon acoustic oscillations
measurements and the local measurements of $H_0$ obtained by the SH0ES
(Supernovae, $H_0$, for the Equation of State of Dark energy) collaboration
analysing the Hubble Space Telescope data. We discuss the alleviation of $H_0$
tension, that is obtained at the price of a phantom-like dark energy equation
of state. We perform a Bayesian evidence analysis to quantify the improvement
of the fit, finding that all the dark energy models considered in this work are
preferred against the $\Lambda$CDM scenario. Finally, among all the
possibilities analyzed, the CPL model is the best one in fitting the data and
solving the $H_0$ tension at the same time. However, unfortunately, this
dynamical dark energy solution is not supported by the baryon acoustic
oscillations (BAO) data, and the tension is restored when BAO data are included
for all the models.
