The steady state cosmology and the cosmological tests

The steady state cosmology had a positive effect on research in cosmology in the 1950s and early 1960s by stimulating work on observational tests (many aimed at disproving the theory). It may have had the negative effect of distracting attention from other issues; one sees in the next chapter that the significance of measurements of the microwave background radiation was first recognized in Zel'dovich's group in the Soviet Union, where the steady state picture received little attention. But the picture was heavily influential elsewhere for reasons that merit our attention.

We noted the main ideas of the steady state cosmology on page 15: the universe is in a steady state of expansion, and continual creation of matter provides the material for the formation of young galaxies that fill the spaces between the older ones as they move apart, keeping the mean number density of galaxies constant.36 This model was particularly well suited to the state of research in cosmology in the 1950s because it makes definite predictions that one might design observational programs to test. An example is the comparison of appearances of nearby galaxies with those observed at great distance. Distant galaxies are observed as they were in the past, because of the light travel time. In the big bang model distant galaxies, being younger, may be expected to look different from their nearby counterparts. In the steady state model distant and nearby galaxies are the same mix of young and old. That led Bondi (1960b) to state that if distant galaxies were observed to be systematically different from those observed nearby then "the steady-state theory is stone dead."

Here was an interesting opportunity: compare the appearances of nearby and distant galaxies, and perhaps find a critical test of ideas about the nature

36 The model assumes homogeneity, isotropy, and a metric theory of spacetime. This means spacetime can be represented by the Robertson—Walker line element in equation (G.4) on page 526. Since the Hubble parameter a/a = H has to be constant in a universe in a steady state the expansion parameter has to scale as a a eHt. The physical curvature of a space section at fixed world time is (aR)-2, and to make that constant we require R-2 = 0. The line element thus is fixed up to one locally measurable constant, H, to ds2 = dt2 _ e2Ht(dx2 + dy2 + dz2). (3.17)

This happens to be one of the solutions de Sitter (1917) found (in a different coordinate labeling) for a universe that is empty except for Einstein's cosmological constant A, though there is no A in the steady state model. Equation (3.17) also is close to the situation in the present-day universe because the mass density is low and space curvature is small. In the limit of negligibly small mass density (where A in equation 2.5 is dominant) H2 = A/3. Equation (3.17) also applies to the inflation scenario for the very early universe, but with a much larger value of H.

of our universe. There are apparently young galaxies nearby. Hoyle and Narlikar (1962) took that as an argument for the steady state picture, with ongoing creation of galaxies. Gamow (1954), on the other hand, made the now generally accepted point that the colors of most nearby galaxies are much the same, consistent with a close to uniform age of most of the stars in most of the present-day galaxies, and inconsistent with the broad mix of ages of galaxies in the steady state picture.

Another aspect of the age issue is that in a big bang cosmology the universe has expanded from densities and temperatures so large that stars could not have existed. That means the oldest stars have to be younger than the time taken for the universe to expand from high density to its present state. We noted on page 15 that this expansion time might naturally be expected to be about equal to the Hubble time, H-1, where H0 is Hubble's constant (defined in equation 2.1).37 In the 1930s errors in estimates of distances to galaxies led to an underestimate of H-1 by a factor of about 8. That made it awkward to reconcile a big bang age of the universe with the radioactive decay ages of mineral deposits on Earth and in meteorites.38 In the steady state cosmology there are galaxies of all ages, but that does not help much because the mean age of a galaxy is just one-third of H-1. (It is an interesting exercise to show this, following the discussion in footnote 36.) As Gamow remarked, it is awkward to argue that the Milky Way is older than H-1, as would be required to reconcile radioactive decay ages of minerals with the short Hubble time, because this galaxy looks like other nearby spirals, not much older. By 1960 the major errors in the galaxy distance scale had been identified, and Sandage (1958) had arrived at a larger value for H-1 (close to what was later established by the methods in Chapter 5 and the Appendix). In the second edition of Cosmology, Bondi (1960a) greeted this with the comment "it is not easy to appreciate now the extent to which for more than fifteen years all work in cosmology was affected and indeed oppressed by the short value" of the Hubble time H-1.

Sandage (1961) concluded that with the new value of H-1 the big bang cosmology could be older than the oldest stars, but that the fit is tight and might require the postulate of a positive cosmological constant A (as

37 In an expanding model universe with A = 0 and negligibly small mass density the time to since the big bang is equal to the Hubble time H—1. If A = 0 a significant mass density slows the expansion, making to less than H—1. In the Einstein—de Sitter model to = 2H—1 /3. A positive A acts in the opposite way, increasing to. In the cosmology established by the beginning of the 21st century the effects of mass density and A about cancel, making to ~ H—1.

38 Hubble's (1936) distance estimates indicated H—1 = 1.8 billion years. Patterson's (1955) measurements of the decay of uranium to lead isotopes showed that Earth and the asteroids are about 4.5 billion years old.

discussed in footnote 37). Sandage anticipated what happened: the evidence collected in Chapter 5 convincingly shows the effect of a positive A. But the central point in the 1960s was that observations of distant galaxies and the measurements of isotope abundances accumulated by radioactive decay in minerals in the Solar System yield similar ages. The coincidence from such very different observations encouraged at least some to think that there might be something to this expanding universe concept. A set of coincidences of this sort from a considerable variety of measurements is presented in the summary of cosmological tests in Section 5.4.

Another influential - and controversial - opportunity to challenge the steady state cosmology was based on the counts of galaxies detected by radio telescopes. Some galaxies are very strong sources of radio radiation, so they can be seen at great distances, where the properties of spacetime can affect what is observed.

Consider first a simple case: suppose the universe is not expanding, has the flat geometry of Euclid, and contains a uniform spatial distribution of galaxies that are not evolving. Then the count, N(>S), of galaxies that appear brighter than S (that is, S is the rate of arrival of radiation energy from the source per unit collecting area of the telescope) varies with S as39

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