Hubble and the Constant, the Next (and the Next…) Generation

A. Riess (ariess[at]

Our understanding of the Hubble constant has been refined by successive generations, while often teaching us something new about the Universe. The first estimates circa 1929 yielded a value of 500 km sec–1 Mpc–1 for the expansion rate which, if rewound to an initial singularity, implied the Universe was younger than the age estimated for the Earth and Sun. This discrepancy was resolved by the discovery in the 1950s of differences between successive generations of stars used to make distance measurements. In the 1990s the Hubble Space Telescope (HST) was launched with a mission goal to resolve the "50-or-100" discrepancy for H0 and reach 10% precision. Efforts spearheaded by the HST Key Project (Freedman et al. 2001) using WFPC2 to observe Cepheids in a wide-range of secondary distance indicators, and a second collaboration observing Cepheids in hosts of nearby SN Ⅰa (Sandage et al. 2006), resulted in values in the middle of that range. These values required the newly discovered cosmic acceleration to be compatible with the ages of the oldest stars. Yet the mystery of dark energy and its role in conjunction with new CMB data to predict the value of H0 to better than 1% precision has motivated a new generation of local measurements with HST to approach a 1% "end-to-end" test of the enigmatic Cosmological Model.

The best-established local method and one which can approach 1% precision comes from building a ''distance ladder'' using simple geometry to calibrate the luminosities of specific star types, pulsating (Cepheid variables) and exploding (Type Ⅰa supernovae or SN Ⅰa), which can be seen at great distances where their redshifts directly measure cosmic expansion. The prior generation's efforts using HST's WFPC2 were severely limited in range (to D = 20–25 Mpc to measure Cepheids) to a sample of just a few local SN Ⅰa with high quality data with new examples occurring just once per decade. The precision by this route is largely limited by the distance-measuring precision of a single SN Ⅰa (5–6%) divided by the square root of the sample size. HST's ACS and WFC3 more than doubled this range to provide new candidates once every year or two.

The SH0ES Project starting in 2005 advanced this method by: 1) increasing the sample of high quality calibrations of SN Ⅰa by Cepheids from a few to 19 (Riess et al. 2016); 2) increasing the number of independent geometric calibrations of Cepheids from two to five (Riess et al. 2018a,b) including by extending the range of parallax measurements to Cepheids using the spatial scanning technique of WFC3; 3) measuring the fluxes of Cepheids with geometric distance measurements and those in supernova hosts with the same instrument to negate calibration errors (Riess et al. 2019); and 4) measuring Cepheids in the near-infrared to reduce systematics related to dust and metallicity. Improved geometric distance estimates to the Large Magellanic Cloud (LMC) using detached eclipsing binaries (Pietrynzski et al. 2019), to NGC 4258 using water masers (Reid et al. 2019) and to Milky Way Cepheids from ESA Gaia parallaxes have greatly aided this work. The present result is H0 = 73.5 ± 1.4 km s–1 Mpc–1 (see Fig. 1) which is in 4.2σ higher than the value of 67.5 ± 0.4 km s–1 Mpc–1 predicted by Planck with ΛCDM setting up the present and oft-called "Hubble Tension" or Early-vs-Late Universe discrepancy.  (For reference, the final result of the Key Project in 2001 was 72 ± 8 km s–1 Mpc–1 and later recalibrated using improved geometric distances to 74.3 ± 2.2 km s–1 Mpc–1, Freedman et al. 2012).

distance ladder at different magnifications
Figure 1: Geometry-Cepheids-SN Ⅱa distance ladder from Riess et al. (2019).

This difference is potentially far more interesting and consequential than the factor-of-two debates of the 1980s because this discrepancy is seen across cosmic time and therefore might provide hints of a new wrinkle in the cosmological model. Concerns about unknown systematic errors are largely addressed by independent approaches applied at both ends of the discrepancy, which consistently yield 67–68 from the Early Universe and a range of 70–75 locally as shown in Figure 2 (see also a review by Verde, Treu, & Riess 2019), thus requiring multiple, independent, and still undiscovered systematic errors to resolve. HST has contributed vital data for a number of the local methods including measurements of the Tip of the Red Giant Branch (Freedman et al. 2019) and Oxygen-rich Miras (Huang et al. 2019) as shorter-range alternatives to Cepheids and of Quasar lensing (Wong et al. 2019) and Surface Brightness Fluctuations as an alternative to SN Ⅰa. These measurements are far from complete (and surely never will be!), but have improved rapidly in the last decade. In the very near term, we can anticipate a doubling of the Cepheid-calibrated SN Ⅰa sample to 38 by the SH0ES Team and the 3rd parallax data release from Gaia which should improve the local result to a precision better than 1.5% or ±1 km s–1 Mpc–1. It is hard to imagine reaching such precision when HST was first launched.

compilation of papers measuring distance
Figure 2: Compilation of measurements of H0, figure from Di Valentino et al. (2020, submitted).

If the Universe fails this end-to-end test (it surely hasn’t passed), what could we learn? Would this be evidence of "New Physics'' in the cosmos at play? A wide range of theoretical solutions with varying degrees of success have been proposed. Dark Energy with an equation of state lower than vacuum energy (i.e., w < –1) could produce stronger acceleration and explain the discrepancy, but this possibility is disfavored by high-redshift SNe Ⅰa and Baryon Acoustic Oscillation measurements. If we lived near the middle of a vast and deep void in the large-scale structure of the Universe, this could cause excess, local expansion. However, the odds of a void this large occurring by chance is incredibly low, exceeding 10σ (Wu & Huterer 2017) and is also ruled out empirically by the lack of a large inflection in the expansion rate with distance from SNe Ⅰa within z < 0.3 (Kenworthy et al. 2019).  

More success has been found by altering the composition of the Universe shortly before the emergence of the CMB. An additional component in ΛCDM such as a new neutrino or scalar field (the latter called Early Dark Energy or EDE) can increase early expansion, decrease the sound horizon of primordial fluctuations and raise the predicted value of H0 depending on the approach used to 70–73 km s–1 Mpc–1 (Poulin et al. 2019; Kreisch et al. 2020; Agrawal et al. 2019) in plausible agreement with the local value. A criticism of EDE or a new particle solution is that its scale (for EDE) or interactions (for neutrinos) must be finely-tuned to succeed, though the same is generally true of other wrinkles in cosmology including inflation and Λ. Also worth keeping an eye on is the lesser Early-vs-Late tension in the value of σ8, the local clumpiness of matter, which may have a related explanation. The work on the theoretical and observational side of this problem is not done, but will surely be completed by the next generation. 


Agrawal, P., et al. 2019,  arXiv:1904.01016 

Freedman, W., et al. 2001, ApJ, 533, 47

Freedman, W., et al. 2012, ApJ, 758, 24

Freedman, W., et al. 2019, ApJ, 882, 34

Huang, C. D., et al. 2020, ApJ, 889, 5

Kenworthy, W. D., Scolnic, D. & Riess, A. G. 2019, ApJ, 875, 145

Kreisch, C., Cyr-Racine, F. Y. & Doré, O. 2020, PhRevD, 101, 12

Pietrzyński, G., et al. 2019, Nature, 567, 200

Poulin, V., et al. 2019, PhRvL, 122, 1301

Reid, M. J., Pesce, D. W. & Riess, A. G. 2019, ApJ, 86, L27

Riess, A. G., et al. 2016, ApJ, 826, 56

Riess, A. G., et al. 2018a, ApJ, 855, 136

Riess, A. G., et al. 2018b, ApJ, 861, 126

Riess, A. G., et al. 2019, ApJ, 876, 85

Sandage, A., et al. 2006, ApJ, 653, 843

Verde, L., Treu, T. & Riess, A. G. 2019, Nature Astronomy 3, 891

Wong, K., et al. 2019, MNRAS, 498, 1420

Wu, H.-Y., & Huterer, D. 2017, MNRAS, 471, 4946