Cosmology Intertwined II: The Hubble Constant Tension
  The current cosmological probes have provided a fantastic confirmation of the
standard $\Lambda$ Cold Dark Matter cosmological model, that has been
constrained with unprecedented accuracy. However, with the increase of the
experimental sensitivity a few statistically significant tensions between
different independent cosmological datasets emerged. While these tensions can
be in portion the result of systematic errors, the persistence after several
years of accurate analysis strongly hints at cracks in the standard
cosmological scenario and the need for new physics. In this Letter of Interest
we will focus on the $4.4\sigma$ tension between the Planck estimate of the
Hubble constant $H_0$ and the SH0ES collaboration measurements. After showing
the $H_0$ evaluations made from different teams using different methods and
geometric calibrations, we will list a few interesting new physics models that
could solve this tension and discuss how the next decade experiments will be
crucial.
