Dynamical Dark sectors and Neutrino masses and abundances
  We investigate generalized interacting dark matter-dark energy scenarios with
a time-dependent coupling parameter, allowing also for freedom in the neutrino
sector. The models are tested in the phantom and quintessence regimes,
characterized by an equation of state $w_x<-1$ and $w_x>-1$, respectively. Our
analyses show that for some of the scenarios the existing tensions on the
Hubble constant $H_0$ and on the clustering parameter $S_8$ can be
significantly alleviated. The relief is either due to \textit{(a)} a dark
energy component which lies within the phantom region; or \textit{(b)} the
presence of a dynamical coupling in quintessence scenarios. The inclusion of
massive neutrinos into the interaction schemes does not affect neither the
constraints on the cosmological parameters nor the bounds on the total number
or relativistic degrees of freedom $N_{\rm eff}$, which are found to be
extremely robust and, in general, strongly consistent with the canonical
prediction $N_{\rm eff}=3.045$. The most stringent bound on the total neutrino
mass $M_{\nu}$ is $M_{\nu}<0.116$ eV and it is obtained within a quintessence
scenario in which the matter mass-energy density is only mildly affected by the
presence of a dynamical dark sector coupling.
