Chapter 16: The Expanding Universe

Redshift and Blueshift of light by Doppler effect.

How do astronomers estimate the Hubble constant? It is a very difficult research undertaking. Measuring the redshift for a galaxy is the easy part. The hard part is the measurement of distance. Astronomers must avoid galaxies that are too close to the Milky Way because they are bound to each other by gravity and do not take part in the general expansion. They also must avoid galaxies elsewhere in space that are bound in a group or cluster, because they are all at roughly the same distance. Otherwise, it does not matter how the galaxies are selected. Since the expansion is isotropic, the same Hubble relation should be measured in every direction in the sky. Once the redshift and distance of a galaxy have been measured, each galaxy can be plotted as a point on a Hubble relation. The slope of the line that gives the best fit to the data is the Hubble constant.

S represents an ideal source of electromagnetic radiation and A represents an arbitrary segment of the surface of a sphere of radius r.

All methods of distance determination need an accurate calibration at small distances. This calibration sets the luminosity of each new distance indicator — all of the uncertainty in the Hubble constant comes from this procedure. Once the calibration is known, relative distances are easy to calculate using the inverse square law. You can understand distance calibration by analogy from everyday experience. Suppose you were measuring distances around your house using a tape measure. The accuracy of all your measurements would depend on how accurately an inch had been defined or calibrated when the tape measure was made at the factory. Or suppose you were trying to measure the distance between two towns using the odometer in your car. The accuracy of your measurement would depend on how accurately the circumference of your wheel had been calibrated at the factory since an odometer essentially counts wheel rotations. Likewise, in astronomy, the bedrock of all astronomical distance measurements is parallax. Trigonometry has been used to measure the distances to many stars in the neighborhood of the Sun; the calibration of all other distance indicators depends on this information.

Astronomers have not yet reached a consensus as to the value of the Hubble constant. The subject of the distance scale has a long history of controversy and unrecognized systematic errors. Hubble's first measurements yielded a very steep slope and a high value for H₀: 540 km/s/Mpc. This high value was alarming because it implied such a rapid expansion that the universe had to be younger than the well-measured age of the Earth! It turns out that Hubble had used an erroneous calibration of the Cepheid luminosity. During a vast observational effort that started in the mid-1970s, using hundreds of nights of time on large telescopes, published values of the Hubble constant ranged from 50 to 100 km/s/Mpc.

SN1987A in the Large Magellanic Cloud.

Why this uncertainty of a factor of two? One reason is dust. When we look out to the galaxies, we look through a veil of stars and dust in the disk of our own Milky Way. This relatively nearby dust dims and reddens the light from distant galaxies. Dust makes a galaxy of a particular luminosity appear farther away than if it were viewed through no dust. The radial velocity is unaffected. The result is a lower value of the Hubble constant. Moreover, Cepheids and supernovae in distant galaxies are dimmed by dust in the galaxy that contains them as well as by patchy dust in our own galaxy. While all researchers agree that this effect is important, they disagree on the size of the correction for dust. Another cause of uncertainty is our imperfect understanding of many distance indicators. Our knowledge of the Hubble constant is only as good as our understanding of the physics that sets the luminosity of a distance indicator.

Virgo Cluster

Despite a checkered history, recent measurements have converged on a relatively narrow range for the Hubble constant. Most observations are consistent with an H₀ value of 71 km/s/Mpc. The measurement error on this number is about 5%. (Of course, the possibility of unrecognized systematic error remains.) What does this mean in everyday units? It means that galaxies are being carried away from us by the expansion of space at a rate of 22 km/s or 22 x (3/5) x 3600 = 47,500 mph for every million light-years increase in distance! This number has an uncertainty of about 5%, so we can quote it as 71 ± 4 km/s/Mpc. In other words, it is unlikely that the Hubble constant is much lower than 67 km/s/Mpc or much higher than 75 km/s/Mpc. The fact that many different measurement techniques give a similar expansion rate is a wonderful validation of our basic understanding of how the universe works.

Recently, this pleasing convergence of measurements has come under greater scrutiny. As the data get more precise, different methods are starting to yield significantly different answers. Late universe measurements based on the distance ladder and Cepheid variables give Hubble constant values around 73 kn/s/Mpc while early universe measurements based on the microwave background radiation give Hubble constant values around 68 km/s/Mpc. This persistent discrepancy has been called the "Hubble tension." As more methods are brought to bear on the problem, the situation has got messier, but the tension remains. One possible explanation is that we live near a huge galaxy void, which would skew the local Hubble constant to higher values. A more radical possibility is that new physics beyond the standard cosmological model is needed. A more mundane possibility is that unrecognized systematic errors in one or more of the techniques are causing the disagreement. Currently, there is no resolution and the research continues.