Can the H₀ tension be resolved in extensions to ΛCDM cosmology?

We wish to investigate whether there is an extension to the base ΛCDM cosmology that can resolve the tension between the Planck observation of the cosmic microwave background anisotropies and the local measurement of the Hubble constant. We consider various plausible extended models in this work, and we use the Planck 2015 observations, combined with the baryon acoustic oscillation data, the JLA type Ia supernovae data, and the local measurement of the Hubble constant (by Riess et al. in 2016), to make an analysis. We find that the holographic dark energy plus sterile neutrino model can reduce the tension to be at the 1.11σ level, but this model is obviously not favored by the current observations. Among these extended models, the ΛCDM+N_eff model is most favored by the current observations, and this model can reduce the tension to be at the 1.87σ level. By a careful test, we conclude that none of these extended models can convincingly resolve the H₀ tension.