Cosmology with Galaxy Clusters: I. Mass Measurements and Cosmological   Parameters
  Under the assumption that the gas mass fraction of galaxy clusters estimated out to an outer hydrostatic radius is constant, it is possible to constrain the cosmological parameters by using the angular diameter distance relation with redshift. We applied this to a sample of galaxy clusters from redshifts of 0.1 to 0.94, for which published gas and total masses are available from X-ray data. After scaling the gas fraction values to the r_500 radius (Evrard, Metzler & Navarro 1996), we find an apparent decrease in gas fractions at high redshifts, which can be scaled back to the mean gas fraction value at z ~ 0.1 to 0.2 of (0.060 \pm 0.002) h^{-3/2}, when \Omega_m = 0.55^{+0.35}_{-0.23} (1-\sigma statistical error, \Omega_m + \Omega_{\Lambda} =1). However, various sources of systematic errors can contribute to the change in gas mass fraction from one cluster to another, and we discuss such potential problems in this method. 
Asantha R. Cooray (Univ. of Chicago)