The trouble with H₀

Abstract

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 σ. 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 distance measurements 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 ΛCDM 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 × 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.