We discuss the measurements of the galaxy cluster mass functions at z≈ 0.05 and z≈ 0.5
using high-quality Chandra observations of samples derived from the ROSAT PSPC All-Sky
and 400 deg 2 surveys. We provide a full reference for the data analysis procedures, present
updated calibration of relations between the total cluster mass and its X-ray indicators (TX, M
gas, and YX) based on a subsample of low-z relaxed clusters, and present a first
measurement of the evolving LX–M tot relation (with M tot estimated from YX) obtained from�…

Chandra observations of large samples of galaxy clusters detected in X-rays by ROSAT
provide a new, robust determination of the cluster mass functions at low and high redshifts.
Statistical and systematic errors are now sufficiently small, and the redshift leverage
sufficiently large for the mass function evolution to be used as a useful growth of a structure-
based dark energy probe. In this paper, we present cosmological parameter constraints
obtained from Chandra observations of 37 clusters with< z>= 0.55 derived from 400 deg 2�…