The abundance of high-redshift galaxy clusters depends sensitively on the
matter density \OmM and, to a lesser extent, on the cosmological constant
Λ. Measurements of this abundance therefore constrain these fundamental
cosmological parameters, and in a manner independent and complementary to other
methods, such as observations of the cosmic microwave background and distance
measurements. Cluster abundance is best measured by the X-ray temperature
function, as opposed to luminosity, because temperature and mass are tightly
correlated, as demonstrated by numerical simulations. Taking advantage of the
sensitivity of XMM-Newton, our Guaranteed Time program aims at measuring the
temperature of the highest redshift (z>0.4) SHARC clusters, with the ultimate
goal of constraining both \OmM and Λ.Comment: To appear in the Proceedings of the XXI Moriond Conference: Galaxy
Clusters and the High Redshift Universe Observed in X-rays, edited by D.
Neumann, F. Durret, & J. Tran Thanh Va