B. The development of ideas
In the classic book, The Classical Theory of Fields, Landau
and Lifshitz (1951,
p. 338) second Einstein's opinion of the
cosmological constant
, 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
.
The continued interest was at least in part driven by indications
that might be
needed to reconcile theory and observations. Here are three examples.
First, the expansion time is uncomfortably short if
= 0.
Sandage's recalibration of the distance scale in the 1960s indicates
H0 
75
km s-1 Mpc-1. If
= 0 this says
the time of expansion from densities too high for stars to have
existed is < H0-1
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 . The
present estimates reviewed below (Sec. IV.B.3)
are not far from these numbers, but still too uncertain for a
significant case for
.
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
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
(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
K0 = 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.
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