Cosmological constraints from the evolution of the cluster baryon mass function at z similar to 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 160 deg(2) 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 Type Ia supernovae near Omega(m) = 0.3 and Lambda = 0.7.