Planck and the local Universe: quantifying the tension
  We use the latest Planck constraints, and in particular constraints on the
derived parameters (Hubble constant and age of the Universe) for the local
universe and compare them with local measurements of the same quantities. We
propose a way to quantify whether cosmological parameters constraints from two
different experiments are in tension or not. Our statistic, T, is an evidence
ratio and therefore can be interpreted with the widely used Jeffrey's scale. We
find that in the framework of the LCDM model, the Planck inferred two
dimensional, joint, posterior distribution for the Hubble constant and age of
the Universe is in "strong" tension with the local measurements; the odds being
~ 1:50. We explore several possibilities for explaining this tension and
examine the consequences both in terms of unknown errors and deviations from
the LCDM model. In some one-parameter LCDM model extensions, tension is reduced
whereas in other extensions, tension is instead increased. In particular, small
total neutrino masses are favored and a total neutrino mass above 0.15 eV makes
the tension "highly significant" (odds ~ 1:150). A consequence of accepting
this interpretation of the tension is that the degenerate neutrino hierarchy is
highly disfavoured by cosmological data and the direct hierarchy is slightly
favored over the inverse.
