  We investigate a phenomenological non-gravitational coupling between dark
energy and dark matter, where the interaction in the dark sector is
parameterized as an energy transfer either from dark matter to dark energy or
the opposite. The models are constrained by a whole host of updated
cosmological data: cosmic microwave background temperature anisotropies and
polarization, high-redshift supernovae, baryon acoustic oscillations, redshift
space distortions and gravitational lensing. Both models are found to be
compatible with all cosmological observables, but in the case where dark matter
decays into dark energy, the tension with the independent determinations of
$H_0$ and $\sigma_8$, already present for standard cosmology, increases: this
model in fact predicts lower $H_0$ and higher $\sigma_8$, mostly as a
consequence of the higher amount of dark matter at early times, leading to a
stronger clustering during the evolution. Instead, when dark matter is fed by
dark energy, the reconstructed values of $H_0$ and $\sigma_8$ nicely agree with
their local determinations, with a full reconciliation between high- and
low-redshift observations. A non-zero coupling between dark energy and dark
matter, with an energy flow from the former to the latter, appears therefore to
be in better agreement with cosmological data.
