Cosmological constraints from evolution of cluster baryon mass function at z~0.5

We present a new method for deriving cosmological constraints based on the evolution of the baryon mass function of galaxy clusters, and implement it using 17 distant clusters from our 160deg2 ROSAT survey. The method uses the cluster baryon mass as a proxy for the total mass, thereby avoiding the large uncertainties of the M_tot-T or M_tot-L_X relations used in all previous studies. Instead, we rely on a well-founded assumption that the M_b/M_tot ratio is a universal quantity, which should result in a much smaller systematic uncertainty. Taking advantage of direct and accurate Chandra measurements of the gas masses for distant clusters, we find strong evolution of the baryon mass function between z>0.4 and the present. The observed evolution defines a narrow band in the Omega_m-Lambda plane, Omega_m + 0.23Lambda = 0.41+-0.10 at 68% confidence, which intersects with constraints from the Cosmic Microwave Background and supernovae Ia near Omega_m=0.3 and Lambda=0.7.