Complementary Measures of the Mass Density and Cosmological Constant

The distance-redshift relation depends on the amount of matter of each typein the universe. Measurements at different redshifts constrain differingcombinations of these matter densities and thus may be used in combination toconstrain each separately. The combination of Omega_0 and Omega_Lambda measuredin supernovae at z<1 is almost orthogonal to the combination probed by thelocation of features in the cosmic microwave background (CMB) anisotropyspectrum. We analyze the current combined data set in this framework, showingthat the regions preferred by the Supernova and CMB measurements arecompatible. We quantify the favoured region. We also discuss models in whichthe matter density in the universe is augmented by a smooth component to givecritical density. These models, by construction and in contrast, are notstrongly constrained by the combination of the data sets.Comment: 10 pages, 4 figures, minor changes to reflect version accepted in ApJ. New SN data included. Minor typos fixe