Can the $H_0$ tension be resolved in extensions to $Λ$CDM cosmology?

TL;DR

This study probes whether extensions to the standard $Λ$CDM cosmology can reconcile Planck 2015 CMB observations with the local $H_0$ measurement. It analyzes a suite of one- and multi-parameter extensions, including dynamical dark energy, dark radiation, and sterile neutrinos, using Planck 2015 together with BAO and JLA data, plus the Riess $H_0$ prior. Through χ² and AIC model comparisons and with CAMB/CosmoMC, it finds that no extended model convincingly resolves the $H_0$ tension: while some variants reduce the tension to the ~1.1–1.9σ level, favorable fits are offset by strong AIC penalties or higher σ8 tensions. The most favorable single-parameter extension, $Λ$CDM+$N_{ m eff}$, slightly alleviates the tension to about $1.87σ$ but does not fully reconcile the datasets, and multi-parameter models rarely improve the overall statistical standing. These results suggest the $H_0$ discrepancy remains robust under the tested extensions, highlighting the need for further observational or theoretical developments.

Abstract

We wish to investigate whether there is an extension to the base $Λ$CDM 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 observation, 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 1.11$σ$ level, but this model is obviously not favored by the current observations. Among these extended models, the $Λ$CDM+$N_{\rm eff}$ model is most favored by the current observations, and this model can reduce the tension to be at the 1.87$σ$ level. By a careful test, we conclude that none of these extended models can convincingly resolve the $H_0$ tension.

Figures (1)

• Figure 1: Two-dimensional marginalized contours in the $w$--$H_{0}$ plane for the $w$CDM model, in the $c$--$H_{0}$ plane for the HDE model, in the $\beta$--$H_{0}$ plane for the $\Lambda (t)$CDM model, and in the $N_{\rm eff}$--$H_{0}$ plane for the $\Lambda$CDM+$N_{\rm eff}$ model, by using the CMB+BAO+JLA+$H_{0}$ data.