989.
The analysis of the Th/U ratio in meteorites and the evolutionary ages of globular clusters favour values of the cosmic age of (19±5)×10
9 yr. This evidence together with a Hubble parameter
H
0>70 km s
–1 Mpc
–1=(14×10
9 yr)
–1 cannot be reconciled in a Friedmann model with =0. It requires a cosmological constant in the order of 10
–56 cm
–2, equivalent to a vacuum density
v
=10
–29 g cm
–3
The Friedmann-Lemaître models (>0) with a hot big-bang have been calculated. They are based on a present value of the baryonic matter density of
0=0.5×10
–30 g cm
–3 as derived from the primordial
4He and
2H abundances.For a Hubble parameter of
H
0=75 km s
–1 Mpc
–1, our analysis favours a set of models which can be represented by a model with Euclidean metric (density parameter
0=1.0, deceleration parameter
q
0=–0.93, age
t
0=19.7×10
9 yr) and by a closed model with perpetual expansion (
0=1.072,
q
0=–1.0, age
t
0=21.4×10
9 yr). A present density parameter close to one can indeed be expected if the conjecture of an exponential inflation of the very early universe is correct.The possible behaviour of the vacuum density is demonstrated with the help of Streeruwitz' formula in the context of the closed model with an inflationary phase at very early times.
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