2003ApJ...590...15V

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 160 deg² 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_Xrelations used in all previous studies. Instead, we rely on a well-founded assumption that the M_b/M_totratio 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 Ω_m-Λ plane, Ω_m+0.23Λ=0.41±0.10 at 68% confidence, which intersects with constraints from the cosmic microwave background and Type Ia supernovae near Ω_m=0.3 and Λ=0.7.