One of the most powerful tests for a non-zero cosmological constant is
provided by a comparison of the expansion and oldest-star ages. To
quote
Carroll, Press and
Turner (1990),
``A high value of
*H*_{0} (> 80
km/s/Mpc, say), combined with no loss of confidence in a value 12-14
Gyr as a *minimum* age for some globular clusters, would
effectively prove the existence of a significant _{}
term. Given such observational results, we know of no convincing
alternative hypotheses.''

In Figure 3, the dimensionless product of
*H*_{0}*t*_{0} is
plotted as a function of . Two
different cases are illustrated:
an open _{} = 0 Universe, and a flat
Universe with
_{} + _{m} = 1. Suppose that both
*H*_{0} and
*t*_{0} are both known to ± 10% (1-, *including
systematic errors*). The dashed and dot-dashed lines indicate
1- and 2- limits, respectively for values of
*H*_{0} =
70 km/sec/Mpc and *t*_{0} = 15 Gyr. Since the two
quantities *H*_{0} and
*t*_{0} are completely independent, the two errors have
been added in
quadrature, yielding a total uncertainty on the product of
H_0*t*_{0} of ± 14% rms. These values of
*H*_{0} and *t*_{0}
are consistent with a Universe where _{} = 0.8,
_{m} = 0.2. The
Einstein-de Sitter model (_{m} = 1,
_{} = 0) is excluded (at
2.5).

Despite the enormous progress recently in the measurements of
*H*_{0} and *t*_{0},
Figure 3 demonstrates
that significant further
improvements are still needed. First, in the opinion of this author,
*total* (including both statistical and systematic) uncertainties
of ± 10% have yet to be achieved for either *H*_{0} or
*t*_{0}. Second, assuming that such accuracies will be
forthcoming in
the near future for *H*_{0} (as the Key Project, supernova
programs
and other surveys near completion), and for *t*_{0} (as
HIPPARCHOS
provides an improved calibration both for RR Lyraes and subdwarfs), it
is clear from this figure that if *H*_{0} is as high as 70
km/sec/Mpc, then accuracies of significantly *better than* ±
10% will be required to rule in or out a non-zero value for
. (If *H*_{0}
were larger (or smaller), this discrimination would be simplified!)