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2.1 Preliminary remarks

As we have seen, in principle a single object whose spectrum reveals its recession velocity, and whose distance or luminosity is accurately known, gives a measurement of the Hubble constant. In practice, the object must be far enough away for the dominant contribution to the motion to be the velocity associated with the general expansion of the Universe (the “Hubble flow”), as this expansion velocity increases linearly with distance whereas other nuisance velocities, arising from gravitational interaction with nearby matter, do not. For nearby galaxies, motions associated with the potential of the local environment are about 200 – 300 km s–1, requiring us to measure distances corresponding to recession velocities of a few thousand km s–1 or greater. These recession velocities correspond to distances of at least a few tens of Mpc.

For large distances, corresponding to redshifts approaching 1, the relation between spectroscopically measured redshift and luminosity (or angular diameter) distance is no longer linear and depends on the matter density Ω m and dark energy density Ω Λ, as well as the Hubble constant. This is less of a problem, because as we shall see in Section 3, these parameters are probably at least as well determined as the Hubble constant itself.

Unfortunately, there is no object, or class of object, whose luminosity can be determined unambiguously in a single step and which can also be observed at distances of tens of Mpc. The approach, used since the original papers by Hubble, has therefore been to measure distances of nearby objects and use this knowledge to calibrate the brightness of more distant objects compared to the nearby ones. This process must be repeated several times in order to bootstrap one’s way out to tens of Mpc, and has been the subject of many reviews and books (see e.g. [125]). The process has a long and tortuous history, with many controversies and false turnings, and which as a by-product included the discovery of a large amount of stellar astrophysics. The astrophysical content of the method is a disadvantage, because errors in our understanding propagate directly into errors in the distance scale and consequently the Hubble constant. The number of steps involved is also a disadvantage, as it allows opportunities for both random and systematic errors to creep into the measurement. It is probably fair to say that some of these errors are still not universally agreed on. The range of recent estimates is from 60 to 75 km s–1 Mpc–1 , and the reasons for the disagreements (in many cases by different analysis of essentially the same data) are often quite complex.


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