A Natural Cosmological Model with Omega_matter <1

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.