Next Contents Previous

B. The development of ideas

1. Early indications of Lambda

In the classic book, The Classical Theory of Fields, Landau and Lifshitz (1951, p. 338) second Einstein's opinion of the cosmological constant Lambda, stating there is "no basis whatsoever" for adjustment of the theory to include this term. The empirical side of cosmology is not much mentioned in this book, however (though there is a perceptive comment on the limited empirical support for the homogeneity assumption; p. 332). In the Supplementary Notes to the English translation of his book, Theory of Relativity, Pauli (1958, p. 220) also endorses Einstein's position.

Discussions elsewhere in the literature on how one might find empirical constraints on the values of the cosmological parameters usually take account of Lambda. The continued interest was at least in part driven by indications that Lambda might be needed to reconcile theory and observations. Here are three examples.

First, the expansion time is uncomfortably short if Lambda = 0. Sandage's recalibration of the distance scale in the 1960s indicates H0 appeq 75 km s-1 Mpc-1. If Lambda = 0 this says the time of expansion from densities too high for stars to have existed is < H0-1 appeq 13 Gyr, maybe less than the ages of the oldest stars, then estimated to be greater than about 15 Gyr. Sandage (1961a) points out that the problem is removed by adding a positive Lambda. The present estimates reviewed below (Sec. IV.B.3) are not far from these numbers, but still too uncertain for a significant case for Lambda.

Second, counts of quasars as a function of redshift show a peak at z ~ 2, as would be produced by the loitering epoch in Lemaître's Lambda model (Petrosian, Salpeter, and Szekeres, 1967; Shklovsky, 1967; Kardashev, 1967). The peak is now well established, centered at z ~ 2.5 (Croom et al., 2001; Fan et al., 2001). It usually is interpreted as the evolution in the rate of violent activity in the nuclei of galaxies, though in the absence of a loitering epoch the indicated sharp variation in quasar activity with time is curious (but certainly could be a consequence of astrophysics that is not well understood).

The third example is the redshift-magnitude relation. Sandage's (1961a) analysis indicates this is a promising method of distinguishing world models. The Gunn and Oke (1975) measurement of this relation for giant elliptical galaxies, with Tinsley's (1972) correction for evolution of the star population from assumed formation at high redshift, indicates curvature away from the linear relation in the direction that, as Gunn and Tinsley (1975) discuss, could only be produced by Lambda (within general relativity theory). The new application of the redshift-magnitude test, to Type Ia supernovae (Sec. IV.B.4), is not inconsistent with the Gunn-Oke measurement; we do not know whether this agreement of the measurements is significant, because Gun and Oke were worried about galaxy evolution. (16)

16 Early measurements of the redshift-magnitude relation were meant in part to test the Steady State cosmology of Bondi and Gold (1948) and Hoyle (1948). Since the Steady State cosmology assumes spacetime is independent of time its line element has to have the form of the de Sitter solution with OmegaK0 = 0 and the expansion parameter in Eq. (27). The measured curvature of the redshift-magnitude relation is in the direction predicted by the Steady State cosmology. But this cosmology fails other tests discussed in Sec. IV.B. Back.

Next Contents Previous