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The discrepancy between Planck data and direct measurements of the currentexpansion rate $H_0$ and the matter fluctuation amplitude $S_8$ has become oneof the most intriguing puzzles in cosmology nowadays. The $H_0$ tension hasreached $4.2\sigma$ in the context of standard cosmology i.e $\Lambda$CDM.Therefore, explanations to this issue are mandatory to unveil its secrets.Despite its success, $\Lambda$CDM is unable to give a satisfying explanation tothe tension problem. Unless some systematic errors might be hidden in theobservable measurements, physics beyond the standard model of cosmology must beadvocated. In this perspective, we study a phantom dynamical dark energy modelas an alternative to $\Lambda$CDM in order to explain the aforementionedissues. This phantom model is characterised by one extra parameter,$\Omega_{pdde}$, compared to $\Lambda$CDM. We obtain a strong positivecorrelation between $H_0$ and $\Omega_{pdde}$, for all data combinations. UsingPlanck measurements together with BAO and Pantheon, we find that the $H_0$ andthe $S_8$ tensions are $3\sigma$ and $2.6\sigma$, respectively. By introducinga prior on the absolute magnitude, $M_B$, of the SN Ia, the $H_0$ tensiondecreases to $2.27\sigma$ with $H_0 = 69.76_{-0.82}^{+0.75}$ km s$^{-1}$Mpc$^{-1}$ and the $S_8$ tension reaches the value $2.37\sigma$ with $S_8=0.8269_{-0.012}^{+0.011}$.

Smoothing the $H_0$ tension with a dynamical dark energy model