LOOK-BACK TIME, THE AGE OF THE UNIVERSE, AND THE CASE FOR A POSITIVE COSMOLOGICAL CONSTANT

We present explicit expressions for the calculation of cosmological lo ok-back time, for zero cosmological constant and arbitrary density par ameter OMEGA, which, in the limit as redshift becomes infinite, give t he age of the universe. The case for non-zero cosmological constant is most easily solved via numerical integration. The most distant object s known at present (approaching redshift z = 5) have implied ages of a lmost-equal-to 1-2 Gyr after the Big Bang. The range of such age is na rrow, in spite of a variety of cosmological models one might choose. W e give a graphical representation of a variety of cosmological models and show that a wide range of Hubble constants and values of the age a nd density of the universe compatible with modem studies are consisten t with adoption of a positive cosmological constant.