H0LiCOW XIII. A 2.4% measurement of $H_{0}$ from lensed quasars: $5.3σ$ tension between early and late-Universe probes

Abstract

We present a measurement of the Hubble constant ($H_{0}$) and other cosmological parameters from a joint analysis of six gravitationally lensed quasars with measured time delays. All lenses except the first are analyzed blindly with respect to the cosmological parameters. In a flat $Λ$CDM cosmology, we find $H_{0} = 73.3_{-1.8}^{+1.7}$, a 2.4% precision measurement, in agreement with local measurements of $H_{0}$ from type Ia supernovae calibrated by the distance ladder, but in $3.1σ$ tension with $Planck$ observations of the cosmic microwave background (CMB). This method is completely independent of both the supernovae and CMB analyses. A combination of time-delay cosmography and the distance ladder results is in $5.3σ$ tension with $Planck$ CMB determinations of $H_{0}$ in flat $Λ$CDM. We compute Bayes factors to verify that all lenses give statistically consistent results, showing that we are not underestimating our uncertainties and are able to control our systematics. We explore extensions to flat $Λ$CDM using constraints from time-delay cosmography alone, as well as combinations with other cosmological probes, including CMB observations from $Planck$, baryon acoustic oscillations, and type Ia supernovae. Time-delay cosmography improves the precision of the other probes, demonstrating the strong complementarity. Allowing for spatial curvature does not resolve the tension with $Planck$. Using the distance constraints from time-delay cosmography to anchor the type Ia supernova distance scale, we reduce the sensitivity of our $H_0$ inference to cosmological model assumptions. For six different cosmological models, our combined inference on $H_{0}$ ranges from $\sim73$-$78~\mathrm{km~s^{-1}~Mpc^{-1}}$, which is consistent with the local distance ladder constraints.

Figures (13)

• Figure 1: Multicolor images of the six lensed quasars used in our analysis. The images are created using two or three imaging bands in the optical and near-infrared from HST and/or ground-based AO data. North is up and east is to the left. Images for B1608$+$656, RXJ1131$-$1231, HE 0435$-$1223, and WFI2033$-$4723 are from H0LiCOW I.
• Figure 2: Marginalized $H_{0}$ for a flat $\Lambda$CDM cosmology with uniform priors. Shown are the $H_{0}$ posterior PDFs for the individual lens systems (shaded curves), as well as the combined constraint from all six systems (black line). The median and 16th and 84th percentiles are shown in the figure legend.
• Figure 3: Same as Figure \ref{['fig:h0_flcdm']} for an open $\Lambda$CDM cosmology.
• Figure 4: $H_{0}$-$\Omega_{\rm k}$ constraint for an open $\Lambda$CDM cosmology. The black contours show the constraints from H0LiCOW alone, while the grey contours show the constraints from Planck alone. The colored contours show constraints from Planck combined with other probes, as shown in the figure legend. Although the H0LiCOW and Planck constraints are not consistent with each other, we show the combination here for completeness. The contour levels represent the 1$\sigma$ and 2$\sigma$ constraints.
• Figure 5: Same as Figure \ref{['fig:h0_flcdm']} for a flat $w$CDM cosmology.