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Hubble Constant: Gravitational-lensing measurements push Hubble-constant discrepancy past 5σ


• 2020: Little is known about what dark matter and dark energy, the dominant components of the universe, really are. But the standard model of Big Bang cosmology, known as ΛCDM (Lambda Cold Dark Matter), incorporates how they outwardly behave. Dark energy, the model presumes, takes the form of a cosmological constant Λ, a constant energy density per unit volume of vacuum. Dark matter, meanwhile, is nonrelativistic (or cold; the CDM stands for “cold dark matter”), and it interacts with itself and with ordinary matter only via gravity and possibly the weak force. 1)

With just a handful of free parameters, ΛCDM is appealing in its simplicity, and it generally agrees well with observations of the universe. But an exception is emerging in the Hubble constant H0', the universe’s present rate of expansion.

For ΛCDM to predict a value for H0, its free parameters must be constrained—for example, by a map of the cosmic microwave background (CMB), a picture of the spatial structure of the early universe. From 2009 to 2013, the Planck observatory measured the CMB with great resolution and precision; its map, combined with ΛCDM, yields an H0 of 67.4 ± 0.5 km/s/Mpc (Mega parsec ). 2) The structure of the early universe can also be inferred from the distribution of galaxies today (see the article by Will Percival, Physics Today, December 2017, page 32); that approach gives the same prediction for H0, albeit with wider error bars.

But H0 can also be calculated directly from the distances to various astronomical objects and the velocities at which they’re apparently receding from Earth. (See the article by Mario Livio and Adam Riess, Physics Today, October 2013, page 41.) And direct measurements disagree with the ΛCDM value. The SH0ES (Supernova, H0, for the Equation of State of Dark Energy) collaboration has been honing in on an H0 measurement using so-called standard candles: type Ia supernovae and Cepheid variable stars, whose luminosities are known. The team’s latest H0 value, 74.0 ± 1.4 km/s/Mpc (Megaparsec), differs from the ΛCDM value by 4.4 standard deviations. 3)

A difference of that magnitude, although unlikely to arise by chance alone, could still be due to some unappreciated systematic uncertainty in SH0ES’s methodology. That explanation, however, is starting to look much less likely in light of new work from the H0LiCOW (H0 Lenses in COSMOGRAIL’s Wellspring) collaboration, led by Sherry Suyu, which uses gravitationally lensed quasars to independently measure H0. In 2017 the collaboration published a first result based on three lensed quasars (reference [4)]; see also Physics Today, April 2017, page 24). The current work, with key contributions by Kenneth Wong and Geoff Chen, extends the analysis to six quasars.4 The result, 73.3 + 1.7 - 1.8 km/s/Mpc, agrees well with the SH0ES value. Combining the SH0ES and H0LiCOW measurements gives an H0 of 73.8 ± 1.1 km/s/Mpc, which is 5.3σ different from the ΛCDM prediction.

Lensing measurements

The theoretical basis for H0LiCOW’s method, called time-delay cosmography, dates back to a 1964 paper by Norwegian astrophysicist Sjur Refsdal. 5) But not until decades later did telescopes have the capability to implement it. When a quasar or other distant, luminous object lies directly in line with a massive foreground galaxy, its light can be so strongly bent that it appears to Earth-based observers as multiple images. Because the light in each image traverses a path of a different length and a different gravitational potential, as shown in Figure 1, any fluctuation in the quasar’s intensity shows up in the lensed images at different times.


Figure 1: Strong Gravitational Lensing by a foreground galaxy can cause a quasar to appear as several distinct images. Observing the relative time delays among those images provides information about the combination of distances between Earth, the lensing galaxy, and the quasar. Given that the angles θ1and θ2are small, the difference in path lengths shown here is proportional to DdDs/Dds; the difference in light travel time, which includes the effects of general relativity and the universe's expansion, is proportional to that same value (image credit: Freddie Pagani)

Refsdal’s insight was that measuring those time differences (which are on the order of weeks) and the images’ angular deflections (on the order of arcseconds) provides crucial information about the absolute distances to the quasar and the foreground galaxy. The measurement doesn’t directly yield Dd (the distance from Earth to the galaxy), Ds (the distance from Earth to the quasar), or Dds (the distance from the galaxy to the quasar), but it does constrain their combination, which is enough information to calculate H0 from the objects’ known redshifts.

Earth-based telescopes suffice to resolve the lensed images and monitor their time delays. For years, the COSMOGRAIL (Cosmological Monitoring of Gravitational Lenses) collaboration has employed 1- to 2-m telescopes around the world to keep an eye on dozens of confirmed lensed quasars; some of the recorded light curves are shown in Figure 2.


Figure 2: Light curves from the four lensed images of the quasar shown in Figure 1, collected over 13 years by five telescopes from the COSMOGRAIL (Cosmological Monitoring of Gravitational Lenses) collaboration. Fluctuations in the quasar’s intensity appear first in images A and C, then in image B, and finally, about two weeks later, in image D. (adapted from ref. 4)

Measuring the time delays is just one piece of the puzzle. Another crucial ingredient in the H0 calculation is the lensing galaxy’s mass distribution, which is needed to calculate the deflection angles (which can’t be directly measured, because the quasar’s true position on the sky is unseen) and the gravitational effects on the light travel time for each image. The mass distribution isn’t observable, but it can be modeled from the precise positions and shapes of the lensed images. An effective model requires high-resolution images from the Hubble Space Telescope.

It also requires some good judgement. The choice of when to stop adjusting the mass-distribution model requires a subjective assessment of how well the model agrees with the observed data. The H0LiCOW researchers worried that their decisions might be influenced, even subconsciously, by the value of H0 they were hoping to get. So they developed a technique of blind data analysis, whereby they could work on the model and test it against the data without ever seeing the distance or H0 values it would yield. They agreed beforehand that once they settled on a mass distribution that looked good, there was no going back: They’d publish whatever results it yielded with no further modifications.

“Because our analysis was blind, we could have gotten any result,” says Wong. “So it was a bit surprising to find that we were within 1σ of SH0ES.”

Off the distance ladder

SH0ES, meanwhile, has been tackling its own challenges in precisely determining H0. Type Ia supernovae, which are luminous enough to be seen at great distances, are extremely effective tools for measuring relative cosmic distances: Their peak luminosities are nearly all the same, so supernovae that appear dimmer must be farther away. From the slight curve in the relationship between their distances and velocities (inferred from their redshifts) came the Nobel-winning discovery that the expansion of the universe is accelerating (see Physics Today, December 2011, page 14). That determination, however, was made without knowing the absolute distance to any of the supernovae under study, so it didn’t yield a precise value of the present-day expansion rate H0.

To convert the relative distances into absolute ones, astronomers use a hierarchy of measurements called the cosmic distance ladder (see the article by Daniel Holz, Scott Hughes, and Bernard Schutz, Physics Today, December 2018, page 34). The distances to nearby objects, within a thousand parsecs or so, can be accurately measured using the geometric method of parallax. But supernovae of any type are rare events, and there hasn’t been one close enough to Earth for many hundreds of years. Cepheid variable stars can bridge that gap. They’re both numerous enough to be well represented near Earth and bright enough to be visible at the same distances as the nearest supernovae. As discovered by Henrietta Leavitt a century ago, Cepheids’ luminosities are related to their pulsation periods, so their relative distances can be inferred from their apparent brightness.

SH0ES has been shoring up the links between parallax, Cepheids, and supernovae, and other groups have checked and rechecked them. But there remained the possibility that some aspect of the underlying physics—of supernova evolution, Cepheid pulsation, or the telescopes used to observe them—wasn’t understood as well as astronomers thought it was.

It’s important, therefore, that H0LiCOW and SH0ES get the same answer from independent methods. SH0ES’s measurement has nothing to do with gravitational lensing or modeling of galaxy mass distributions, and H0LiCOW’s has nothing to do with the mechanisms of Cepheids or supernovae. If SH0ES’s result is marred by a systematic error, H0LiCOW’s analysis would have to coincidentally include a different error of almost exactly the same magnitude and sign.


In high-energy physics, a signal with statistical significance of 5σ is the threshold for claiming discovery of a new particle or effect. (See, for example, Physics Today, September 2012, page 12, and August 2019, page 14.) The statistical meaning of a 5σ result is the same in all contexts: Assuming a Gaussian distribution of measurement fluctuations, there’s a 1 in 3.5 million chance that the result could arise by statistical fluctuations alone, in the absence of any underlying effect.

But cosmologists so far have been reluctant to declare that the tension in H0 measurements must be a sign of physics beyond the ΛCDM model, in part because it’s not at all clear what that physics would be. There aren’t many ways the ΛCDM model could be modified that would both close the H0 gap and maintain the model’s agreement with all other measurements. Some of the possibilities theorists are exploring include dark radiation (relativistic dark particles, such as sterile neutrinos, whose wavelengths get stretched as the universe expands), non-Newtonian modifications to gravity, or a dark energy that’s not constant. But there’s no specific evidence, yet, of any of them, and a complete theoretical picture remains elusive.

The H0LiCOW researchers are working on adding more quasars to their analysis, with the goal of reducing their measurement uncertainty below 1%, or 0.7 km/s/Mpc. If their H0 value remains unchanged, such a measurement would be 5σ different from the ΛCDM on its own, independent of SH0ES or any other result.

New Distance Measurements Bolster Challenge to Basic Model of Universe

• June 11, 2020: A new set of precision distance measurements made with an international collection of radio telescopes have greatly increased the likelihood that theorists need to revise the “standard model” that describes the fundamental nature of the Universe. 6)

The new distance measurements allowed astronomers to refine their calculation of the Hubble Constant, the expansion rate of the Universe, a value important for testing the theoretical model describing the composition and evolution of the Universe. The problem is that the new measurements exacerbate a discrepancy between previously measured values of the Hubble Constant and the value predicted by the model when applied to measurements of the cosmic microwave background made by the Planck satellite.

“We find that galaxies are nearer than predicted by the standard model of cosmology, corroborating a problem identified in other types of distance measurements. There has been debate over whether this problem lies in the model itself or in the measurements used to test it. Our work uses a distance measurement technique completely independent of all others, and we reinforce the disparity between measured and predicted values. It is likely that the basic cosmological model involved in the predictions is the problem,” said James Braatz, of the National Radio Astronomy Observatory (NRAO).


Figure 3: Artist's conception illustrating a disk of water-bearing gas orbiting the supermassive black hole at the core of a distant galaxy. By observing maser emission from such disks, astronomers can use geometry to measure the distance to the galaxies, a key requirement for calculating the Hubble Constant ( image credit: Sophia Dagnello, NRAO/AUI/NSF)

Braatz leads the Megamaser Cosmology Project, an international effort to measure the Hubble Constant by finding galaxies with specific properties that lend themselves to yielding precise geometric distances. The project has used the National Science Foundation’s Very Long Baseline Array (VLBA), Karl G. Jansky Very Large Array (VLA), and Robert C. Byrd Green Bank Telescope (GBT), along with the Effelsberg telescope in Germany. The team reported their latest results in the Astrophysical Journal Letters. 7)

Edwin Hubble, after whom the orbiting Hubble Space Telescope is named, first calculated the expansion rate of the universe (the Hubble Constant) in 1929 by measuring the distances to galaxies and their recession speeds. The more distant a galaxy is, the greater its recession speed from Earth. Today, the Hubble Constant remains a fundamental property of observational cosmology and a focus of many modern studies.

Measuring recession speeds of galaxies is relatively straightforward. Determining cosmic distances, however, has been a difficult task for astronomers. For objects in our own Milky Way Galaxy, astronomers can get distances by measuring the apparent shift in the object’s position when viewed from opposite sides of Earth’s orbit around the Sun, an effect called parallax. The first such measurement of a star’s parallax distance came in 1838.

Beyond our own Galaxy, parallaxes are too small to measure, so astronomers have relied on objects called “standard candles,” so named because their intrinsic brightness is presumed to be known. The distance to an object of known brightness can be calculated based on how dim the object appears from Earth. These standard candles include a class of stars called Cepheid variables and a specific type of stellar explosion called a Type Ia supernova.

Another method of estimating the expansion rate involves observing distant quasars whose light is bent by the gravitational effect of a foreground galaxy into multiple images. When the quasar varies in brightness, the change appears in the different images at different times. Measuring this time difference, along with calculations of the geometry of the light-bending, yields an estimate of the expansion rate.

Determinations of the Hubble Constant based on the standard candles and the gravitationally-lensed quasars have produced figures of 73-74 km/s (the speed) per megaparsec (distance in units favored by astronomers).

However, predictions of the Hubble Constant from the standard cosmological model when applied to measurements of the cosmic microwave background (CMB) — the leftover radiation from the Big Bang — produce a value of 67.4, a significant and troubling difference. This difference, which astronomers say is beyond the experimental errors in the observations, has serious implications for the standard model.

The model is called Lambda Cold Dark Matter (ΛCDM), where “Lambda” refers to Einstein’s cosmological constant and is a representation of dark energy. The model divides the composition of the Universe mainly between ordinary matter, dark matter, and dark energy, and describes how the Universe has evolved since the Big Bang.

The Megamaser Cosmology Project focuses on galaxies with disks of water-bearing molecular gas orbiting supermassive black holes at the galaxies’ centers. If the orbiting disk is seen nearly edge-on from Earth, bright spots of radio emission, called masers — radio analogs to visible-light lasers — can be used to determine both the physical size of the disk and its angular extent, and therefore, through geometry, its distance. The project’s team uses the worldwide collection of radio telescopes to make the precision measurements required for this technique.

In their latest work, the team refined their distance measurements to four galaxies, at distances ranging from 168 million light-years to 431 million light-years. Combined with previous distance measurements of two other galaxies, their calculations produced a value for the Hubble Constant of 73.9 kilometers per second per megaparsec.

“Testing the standard model of cosmology is a really challenging problem that requires the best-ever measurements of the Hubble Constant. The discrepancy between the predicted and measured values of the Hubble Constant points to one of the most fundamental problems in all of physics, so we would like to have multiple, independent measurements that corroborate the problem and test the model. Our method is geometric, and completely independent of all others, and it reinforces the discrepancy,” said Dom Pesce, a researcher at the Center for Astrophysics | Harvard and Smithsonian, and lead author on the latest paper.

“The maser method of measuring the expansion rate of the universe is elegant, and, unlike the others, based on geometry. By measuring extremely precise positions and dynamics of maser spots in the accretion disk surrounding a distant black hole, we can determine the distance to the host galaxies and then the expansion rate. Our result from this unique technique strengthens the case for a key problem in observational cosmology.” said Mark Reid of the Center for Astrophysics | Harvard and Smithsonian, and a member of the Megamaser Cosmology Project team.

“Our measurement of the Hubble Constant is very close to other recent measurements, and statistically very different from the predictions based on the CMB and the standard cosmological model. All indications are that the standard model needs revision,” said Braatz.

Astronomers have various ways to adjust the model to resolve the discrepancy. Some of these include changing presumptions about the nature of dark energy, moving away from Einstein’s cosmological constant. Others look at fundamental changes in particle physics, such as changing the numbers or types of neutrinos or the possibilities of interactions among them. There are other possibilities, even more exotic, and at the moment scientists have no clear evidence for discriminating among them.

“This is a classic case of the interplay between observation and theory. The Lambda CDM model has worked quite well for years, but now observations clearly are pointing to a problem that needs to be solved, and it appears the problem lies with the model,” Pesce said.

The National Radio Astronomy Observatory is a facility of the NSF (National Science Foundation), operated under cooperative agreement by Associated Universities, Inc.

1) Johanna L. Miller, ”Gravitational-lensing measurements push Hubble-constant discrepancy past 5σ," Physics Today, Vol. 73, No 3, 2020,, URL:, Published by the American Institute of Physics

2) Planck Collaboration: N. Aghanim, Y. Akrami, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini, A. J. Banday,R. B. Barreiro, N. Bartolo, S. Basak, R. Battye, K. Benabed, J.-P. Bernard, M. Bersanelli, P. Bielewicz, J. J. Bock,J. R. Bond, J. Borrill, F. R. Bouchet, F. Boulanger, M. Bucher, C. Burigana, R. C. Butler, E. Calabrese, J.-F. Cardoso, J. Carron, A. Challinor, H. C. Chiang, J. Chluba, L. P. L. Colombo, C. Combet, D. Contreras, B. P. Crill, F. Cuttaia, P. de Bernardis, G. de Zotti, J. Delabrouille, J.-M. Delouis, E. Di Valentino, et al., ”Planck 2018 results. VI. Cosmological parameters,” Astronomy & Astrophysicsmanuscript no. ms, September 24, 2019, URL:

3) Adam G. Riess, Stefano Casertano, Wenlong Yuan, Lucas M. Macri, and Dan Scolnic, ”Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛCDM,” The Astrophysical Journal, Volume 876, Number 1, Published: 7 May 2019, URL:

4) V. Bonvin, F. Courbin, S. H. Suyu, P. J. Marshall, C. E. Rusu, D. Sluse, M. Tewes, K. C. Wong, T. Collett, C. D. Fassnacht, T. Treu, M. W. Auger, S. Hilbert, L. V. E. Koopmans, G. Meylan, N. Rumbaugh, A. Sonnenfeld, C. Spiniello, ”H0LiCOW – V. New COSMOGRAIL time delays of HE 0435-1223: H0 to 3.8 per cent precision from strong lensing in a flat ΛCDM model,” Monthly Notices of the Royal Astronomical Society, Volume 465, Issue 4, March 2017, Pages 4914–4930,

5) Sjur Refsdal, ”On the Possibility of Determining Hubble's Parameter and the Masses of Galaxies from the Gravitational Lens Effect,” MNRAS (Monthly Notices of the Royal Astronomical Society), Volume 128, Issue 4, September 1964, Pages 307–310,, Published: 01 September 1964

6) ”New Distance Measurements Bolster Challenge to Basic Model of Universe,” NRAO News, 11 June 2020, URL:

7) D. W. Pesce, J. A. Braatz, M. J. Reid, A. G. Riess, D. Scolnic, J. J. Condon, F. Gao, C. Henkel, C. M. V. Impellizzeri, C. Y. Kuo, and K. Y. Lo, ”The Megamaser Cosmology Project. XIII. Combined Hubble Constant Constraints,” The Astrophysical Journal Letters, Volume 891, Number 1, Published: 26 February 2020,

The information compiled and edited in this article was provided by Herbert J. Kramer from his documentation of: ”Observation of the Earth and Its Environment: Survey of Missions and Sensors” (Springer Verlag) as well as many other sources after the publication of the 4th edition in 2002. - Comments and corrections to this article are always welcome for further updates (


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