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 Lambda CDM 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 similar to 1: 50. We explore several possibilities for explaining this tension and examine the consequences both in terms of unknown errors and deviations from the Lambda CDM model. In some one-parameter Lambda CDM 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 similar to 1: 150). A consequence of accepting this interpretation of the tension is that the degenerate neutrino hierarchy is highly disfavored by cosmological data and the direct hierarchy is slightly favored over the inverse. (C) 2013 The Authors. Published by Elsevier B.V.