2.3. Establishing the Extragalactic Distance Scale

H₀ is determined by measuring redshifts and distances to galaxies. Redshifts are trivial to measure but distances are difficult to measure. When determining extragalactic distances, there are two routes to take. The conventional route, and the one we focus most on in this discussion, is by means of a distance scale ladder. The Astronomical distance scale ladder works in a bootstrap manner where certain techniques are used over short distance scales to calibrate other techniques to use over longer distance scales. The main problem with this approach is that all errors are cumulative. Thus, the final technique used to derive distances to galaxies for purposes of determining H₀ carries with it all systematic errors that occurred in the previous steps. Each step of the ladder must be free from systematic errors and this requires forming a representative sample of objects for each distance measuring technique. Much of the disagreement about the value of H₀ which is derived in this manner stems from sample selection issues. It is simply impossible to summarize all of the various objections that distance scale practicioneers have to each other's data sets. Most of these objections center around the argument that conspiratorial sample selection effects have combine to produce erroneous results (i.e., the wrong value for H₀).

In addition, its not clear that modern determinations of H₀ have ever been done without a priori prejudice about the age of the Universe As early as 1963, the theory of stellar evolution, combined with color-magnitude diagrams of globular clusters, suggested ages as high as 17 billion years (see Sandage 1963). This naturally leads to values of H₀ 55 km s^-1 Mpc^-1 in order to avoid a potential conflict between the expansion age of the Universe and the age of its oldest stars. Indeed, it is clear from history that the age of the Universe has been used as a constraint on the H₀. Hubble's original determination of H₀, which was later modified by Baade, produced values such that the age of the Universe was now younger than the estimated age of the earth. Since the age of the earth is known with precision, then this is a valid constraint. However, the ages of the oldest stars in our galaxy are not known with precision and hence should never be used to a priori exclude possible values for H₀. Moreover the age of the Universe is only directly related to H₀^-1 in a specific cosmology, one in which = 0. This means that pursuit of H₀ in the absence of prejudice concerning the age of Universe can potentially provide evidence that is not zero. Such a finding would alter our cosmology in a far more profound way than determining the actual value of H₀.

Perhaps the best way to resolve the controversy over H₀ is to develop some physical technique for measuring distances directly. This would have the effect of by-passing the cumbersome distance scale ladder altogether. In theory, these direct methods are rooted in understood physics and immune to issues associated with sample selection. These techniques are beginning to surface but are not sufficiently robust to yet employ in a credible manner. Nevertheless, we discuss some promising techniques (e.g., timing delays associated with gravitational lensing, the Sunyaev-Zeldovich effect) at the end of this chapter. At present, these alternative distance measuring techniques produce results that are fairly model-dependent but which are not inconsistent with the results obtained from the Distance Scale ladder.

Figure 2-1 summarizes the ideology and techniques used in constructing the distance scale ladder. Here it is schematically illustrated that one technique is used to calibrate another technique and so on. In the subsequent discussion, Population I refers to stars in the Galactic disk, which are generally younger and more metal-rich than Population II stars, which occur in the Galactic Halo and in Globular Clusters. The goal is to achieve a representative sample of objects at each step to ensure that the final measure of H₀ is free from systematic bias. As we shall see, this is difficult to achieve.

Figure 2-1: Schematic illustration of the distance-scale ladder approach where different techniques are used over certain distance ranges. To get to larger distances, one technique is used to calibrate another one. Individual galaxies and/or clusters are set at their nominal distances. The use of the Hubble Space Telescope has extended the range of Cepheid-based distances to galaxies considerably. The numbers along the arrow represent the log of the distance in parsecs.