Title: Can interacting dark energy solve the $H_0$ tension?,
Abstract: The answer is Yes! We indeed find that interacting dark energy can alleviate
the current tension on the value of the Hubble constant $H_0$ between the
Cosmic Microwave Background anisotropies constraints obtained from the Planck
satellite and the recent direct measurements reported by Riess et al. 2016. The
combination of these two datasets points towards an evidence for a non-zero
dark matter-dark energy coupling $\xi$ at more than two standard deviations,
with $\xi=-0.26_{-0.12}^{+0.16}$ at $95\%$ CL. However the $H_0$ tension is
better solved when the equation of state of the interacting dark energy
component is allowed to freely vary, with a phantom-like equation of state
$w=-1.184\pm0.064$ (at $68 \%$ CL), ruling out the pure cosmological constant
case, $w=-1$, again at more than two standard deviations. When Planck data are
combined with external datasets, as BAO, JLA Supernovae Ia luminosity
distances, cosmic shear or lensing data, we find good consistency with the
cosmological constant scenario and no compelling evidence for a dark
matter-dark energy coupling.