  Flat cosmological models with a cosmological constant on the order of the
Einstein-de Sitter critical density are enigmatic in the sense that there does
not appear to be any natural explanation for why there should be a cosmological
constant with such a magnitude. As a perhaps more natural alternative we
propose a spatially homogeneous isotropic Omega=1 universe containing cold
matter and with a vacuum energy that varies inversely with the square of the
Robertson-Walker scale parameter. This leads to a cosmological model that in
some ways resembles yet is distinct from an open Friedmann universe with no
cosmological constant. Some possibilities for distinguishing between a flat
universe with a cosmological constant and a flat universe where the vacuum
energy is inversely proportional to the square of the scale parameter are
discussed.
