The trouble with $H_0$

TL;DR

The paper investigates the $H_0$ tension between local $H_0$ measurements and CMB-inferred values, examining (i) possible changes to early-time physics, (ii) alterations to late-time expansion, and (iii) a model-independent reconstruction of the late-time expansion using BAO and SNeIa to determine the low-redshift standard ruler $r_s$. Using Planck data (with and without high-$\ell$ polarization), BAO, SNeIa from JLA, and $H_0$ from Riess, the authors find no compelling evidence for additional relativistic species or dark radiation when high-$\ell$ polarization is included; relaxing early-time constraints can improve but not fully resolve the tension. Their model-independent late-time analyses show that the expansion history remains very close to LCDM for $z<1.3$, and that a consistent $r_s$ value derived from low-redshift data is $r_s=136.7\pm4.1$ Mpc, underscoring that the tension primarily reflects a normalization mismatch between the two anchors ($H_0$ and $r_s$). Overall, the tension appears to be a mismatch in the distance ladder normalization rather than a dramatic departure in the expansion history, with potential resolutions lying in new early-Universe physics or unaccounted systematics in high-$\ell$ polarization data or local $H_0$ measurements.

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 $3σ$. 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 LCDM model. These probes also provide a model insensitive constraint on the low-redshift standard ruler, measuring directly the combination $r_s h$ where $H_0=h \times 100$ km/s/Mpc 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.

Figures (13)

• Figure 1: Marginalised 68% and 95% constraints on $H_0$ from different analysis of CMB data, obtained from Planck Collaboration 2015 public chains Planckparameterspaper, WMAP9 HinshawWMAP_13 (analysed with the same assumptions than Planck) and the results of the work of Addison et al. Addison_2016 and Bonvin et al. H0_holicow. We show the constraints obtained in a $\Lambda$CDM context in blue, $\Lambda$CDM+$N_{\rm eff}$ in red, quasar time-delay cosmography results (taken from H0LiCOW project H0_holicow, for a $\Lambda$CDM model, with and without relying on a CMB prior for $\Omega_{\rm M}$) in green and the constraints of the independent direct measurement of RiessH0_2016 in black. We report in parenthesis the tension with respect to the direct measurement.
• Figure 2: $68$% and $95$% confidence joint constraints in the $H_0$-$Y_{\rm P}^{\rm BBN}$ parameter space for Planck 2015 using temperature and polarization power spectra (left) and without include high $\ell$ polarization data (right). The vertical bands correspond to the local $H_0$ measurement RiessH0_2016. The horizontal black dashed lines correspond to the measurement (mean and 1 and 2 $\sigma$) of the primordial abundance of Aver:2013wba, and in magenta of Izotov_Yp_2014, both from chemical abundances in metal-poor HII regions. The red dotted horizontal line is the 2 $\sigma$ upper limit of the recent measurement of initial Solar helium abundance of Serenelli:2010fk.
• Figure 3: Confidence regions (68% and 95%) of the joint constraints in the $H_0$-$N_{\rm eff}$ parameter space for Planck 2015 data (blue) and Planck 2015 + BAO data (green) using full temperature and polarization power spectra (left) and without including high $\ell$ polarization data (right). Here all species behave like neutrinos when perturbations are concerned. The vertical bands correspond to the local $H_0$ measurement RiessH0_2016.
• Figure 4: CMB temperature ( left), temperature and polarization cross correlation ( right) and polarization ( bottom) power spectra predictions for $\Lambda$CDM (red) and the following extensions: one more neutrino (blue), one scalar field (green), two scalar fields (black) and a illustrative case with extreme (non physical) values of $c^2_s$ and $c^2_{\rm vis}$ with $\Delta N_{\rm eff}=0.1$ (orange).
• Figure 5: Marginalized 68$\%$ and $95\%$ confidence level constraints in the $\Delta N_{\rm eff}$-$H_0$ plane. Left: Planck data including full temperature and polarization power spectra. Right: Excluding high $\ell$ polarisation. We report results using Planck 2015 power spectra (blue), adding CMB lensing (red) and adding also BAO (green). The vertical black bands correspond to the local $H_0$ measurement RiessH0_2016. Note the change in the scale of the y axis in each plot.