A Differential Volume-Redshift Test

The geometry of Freedman-Roberston-Walker cosmological models is fixed by the mass density parameter, Omega_M, and the cosmological constant, Omega_Lambda. The classical volume-redshift cosmological relation is a sensitive Omega=[Omega_M,Omega_Lambda] indicator but its redshift dependence is observationally degenerate with the luminosity or number density evolution of galaxies. Introducing a measurement of the invariant co-moving mass density of the universe reduces the problem of galaxy evolution to a differential measurement between clustered and field galaxies. The cost is a 25% reduction in sensitivity to the Omega's, although this test still remains 50% more Omega sensitive than the magnitude-redshift relation. An implementation of the test as the product of the mass-to-light ratio, M/L, of some clustered systems such as galaxy groups or clusters, with j/rho_c, the normalized luminosity density, is considered. Over the zero to one redshift range the apparent Omega_e(z)=M/L x j/rho_c has a zero point and slope related to Omega_M and Omega_Lambda, respectively. All quantities are used in a differential sense, so that common selection effects, dynamical scale errors, and galaxy evolution effects will largely cancel. The residual differential galaxy evolution between field and the clustered galaxies can be measured from the sample data. Monte Carlo simulations, calibrated with observational data, show that 20 clusters spread over the zero to one redshift range, each having 100 cluster velocities, allows a 99% confidence discrimination between open and closed low density universe models. A similarly distributed sample of about 100 rich clusters, or about 1000 galaxy groups found within a large field survey, will measure Omega_Lambda to about 7% statistical error.