Hubble Space Telescope Counts of Elliptical Galaxies: Constraints on Cosmological Models ?

The interpretation of galaxy number counts in terms of cosmological models is fraught with difficulty due to uncertainties in the overall galaxy population (mix of morphological types, luminosity functions etc.) and in the observations (loss of low surface brightness images, image blending etc.). Many of these can be overcome if we use deep high resolution imaging of a single class of high surface brightness galaxies, whose evolution is thought to be fairly well understood. This is now possible by selecting elliptical and S0 galaxies using Hubble Space Telescope images from the Medium Deep Survey and other ultradeep WFPC2 images. In the present paper, we examine whether such data can be used to discriminate between open and closed universes, or between conventional cosmological models and those dominated by a cosmological constant. We find, based on the currently available data, that unless elliptical galaxies undergo very strong merging since $z \sim 1$ (and/or very large errors exist in the morphological classifications), then flat models dominated by a cosmological constant are ruled out. However, both an Einstein-de Sitter ($\Omega_{0}=1$) model with standard passive stellar evolution and an open ($\Omega_{0}=0.05$) model with no net evolution ({\it i.e.} cancelling stellar and dynamical evolution) predict virtually identical elliptical and S0 galaxy counts. Based on these findings and the recent reportings of $H_{o} \simeq 80$ km/s Mpc/s, we find that the maximum acceptable age of the universe is 13.3 Gyrs and a value of $\leq 9$ Gyrs favored. A flat---$\Lambda \neq 0$---universe is therefore {\it not} a viable solution to the $H_{o}$/globular cluster age problem.