H0LiCOW XIII. A 2.4% measurement of H₀ from lensed quasars: 5.3σ tension between early and late-Universe probes.

We present a measurement of the Hubble constant 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. This time-delay cosmography method is completely independent of both type Ia supernovae (SNe) calibrated by the local distance ladder, as well as observations of the cosmic microwave background (CMB), providing a key independent and complementary constraint.

Our sample of strongly-lensed quasars comprises six systems analyzed to date by H0LiCOW and collaborators. The six lenses are B1608+656 (Suyu et al. 2010; Jee et al. 2019), RXJ1131-1231 (Suyu et al. 2013, 2014; Chen et al. 2019), HE 0435-1223 (Wong et al. 2017; Chen et al. 2019), SDSS 1206+4332 (Birrer et al. 2019), WFI2033-4723 (Rusu et al. 2019), and PG 1115+080 (Chen et al. 2019). Each system has been analyzed using constraints from high-resolution Hubble Space Telescope (HST) and/or ground-based AO imaging data, time-delay measurements from the COSmological MOnitoring of GRAvItational Lenses (COSMOGRAIL; Courbin et al. 2005; Eigenbrod et al. 2005; Bonvin et al. 2018) collaboration and Fassnacht et al. (2002), kinematics from ground-based spectroscopy, and wide-field imaging and spectroscopy to constrain the external convergence. These data allow us to infer the time-delay distance in these systems, as well as the angular diameter distance to the lens in four of the six systems. These quantities are primarily sensitive to H₀, with weaker dependence on other cosmological parameters.

We check that all our lenses can be combined without any loss of consistency by comparing their time-delay distance posteriors in the full cosmological parameter space and measuring the degree to which they overlap. We quantify the consistency by using the Bayes factor, F, in favor of a simultaneous fit of the lenses using a common set of cosmological parameters. We show that none of the 15 possible pairwise combinations of the six lens systems have a Bayes factor F < 1, meaning that all lenses are a consistent realization of the same underlying set of cosmological parameters. If our uncertainties were underestimated, we would not necessarily expect all of our lenses to give statistically consistent results.

In the standard flat ΛCDM cosmology assuming uniform priors on H₀ and Ωm, we find H₀ = 73.3 (-1.8,+1.7) km/s/Mpc, a 2.4% precision measurement. This is higher than the value inferred by Planck CMB observations, which is H₀ = 67.4 +/- 0.5 km/s/Mpc (Planck Collaboration et al. 2018) by 3.1σ and in agreement with the latest result from the Supernova, H₀, for the Equation of State of Dark Energy (SH0ES; Riess et al. 2016) collaboration, which finds H₀ = 74.03 +/- 1.42 km/s/Mpc (Riess et. al 2019) using type Ia supernovae calibrated by the distance ladder.

We explore other, more complex cosmological models as well. We find that allowing for spatial curvature still results in tension with Planck, while a time-varying equation of state parameter (w) leads to degeneracies that may produce useful constraints when combined with other probes. Combining our results with Planck, we test cosmologies with a variable effective number of primordial neutrino species and/or a variable sum of neutrino masses.

We also use the distance measurements from our lens sample to calibrate the distance scale of type Ia supernovae from the joint light-curve analysis (JLA; Betoule et al. 2014) and Pantheon (Scolnic et al. 2018) samples, following the methodology of Taubenberger et al. (2019). We find median H₀ values ranging from ~73-78 km/s/Mpc for a variety of cosmological models. In comparison to the constraints from time-delay cosmography alone, the H₀ from the lenses and SNe are less sensitive to the assumed cosmological model. The tension with Planck in flat ΛCDM is still > 3σ, similar to our result from time-delay cosmography alone.

In combination with the latest SH0ES result, we find a 5.3σ tension between late-Universe determinations of H₀ (H0LiCOW+SH0ES) and Planck CMB measurements for a flat ΛCDM cosmology. Other independent methods anchored in the early Universe, such as the analysis of Abbott et al. (2018b) using a combination of clustering and weak lensing, BAO, and big bang nucleosynthesis (BBN), give similar results to Planck. While systematics still cannot be entirely ruled out and should continue to be explored, recent work has only heightened the tension. There also appears to be a growing dichotomy when the various H₀ probes are split into those anchored by the early-Universe (i.e., CMB), which favor a lower H₀, and those based on late-Universe probes, which favor a higher H₀.

As this tension between early-Universe and late-Universe probes continues to grow, we must examine potential alternatives to the standard flat ΛCDM model. This would be a major paradigm shift in modern cosmology, requiring new physics to consistently explain all of the observational data. We have explored some possible extensions to flat ΛCDM, including spatial curvature, time-varying dark energy (e.g., Di Valentino et al. 2018), and modified neutrino physics such as sterile neutrinos (e.g., Wyman et al. 2014; Gelmini et al. 2019) or self-interacting neutrinos at early times (e.g., Kreisch et al. 2019). Other possible new physics to resolve the discrepancy include an early dark energy component to the Universe that later decays (e.g., Agrawal et al. 2019; Alexander & McDonough 2019; Aylor et al. 2019; Lin et al. 2019; Poulin et al. 2019), primordial non-Gaussianity (e.g., Adhikari & Huterer 2019), and decaying dark matter (e.g., Pandey et al. 2019; Vattis et al. 2019).

While considering the possibility of new physics, we are also continuing to improve the constraints from time-delay cosmography. The current sample of six H0LiCOW systems is already the best-studied sample to date, and a number of additional lenses are being observed with high-resolution imaging (e.g., Shajib et al. 2019) and monitored by COSMOGRAIL. Moving into the future, many new lensed quasars are being discovered in large imaging surveys (e.g., Agnello et al. 2015, 2018a,b; Anguita et al. 2018; Lemon et al. 2018, 2019; Treu et al. 2018). A sample of ~40 lenses is needed to constrain H₀ to the ~1% level (Jee et al. 2016; Shajib et al. 2019), which will be attainable in the near future.