The trouble with H0

We perform a comprehensive cosmological study of the H-0 tension between the direct local measurement and the model-dependent value inferred from the Cosmic Microwave Background. With the recent measurement of H-0 this tension has raised to more than 3 sigma. We consider changes in the early time physics without modifying the late time cosmology. We also reconstruct the late time expansion history in a model independent way with minimal assumptions using distances measures from Baryon Acoustic Oscillations and Type Ia Supernovae, finding that at z < 0.6 the recovered shape of the expansion history is less than 5% different than that of a standard Lambda CDM model. These probes also provide a model insensitive constraint on the low-redshift standard ruler, measuring directly the combination r(s)h where H-0= h x 100 Mpc(-1) km/s and r(s) is the sound horizon at radiation drag (the standard ruler), traditionally constrained by CMB observations. Thus r(s) and H-0 provide absolute scales for distance measurements (anchors) at opposite ends of the observable Universe. We calibrate the cosmic distance ladder and obtain a model-independent determination of the standard ruler for acoustic scale, r(s). The tension in H-0 reflects a mismatch between our determination of r(s) and its standard, CMB-inferred value. Without including high-l Planck CMB polarization data (i.e., only considering the recommended baseline low-l polarisation and temperature and the high l temperature data), a modification of the early-time physics to include a component of dark radiation with an effective number of species around 0.4 would reconcile the CMB-inferred constraints, and the local H-0 and standard ruler determinations. The inclusion of the preliminary high-l Planck CMB polarisation data disfavours this solution.