We discuss the measurements of the galaxy cluster mass functions at z \approx 0.05 and z \approx 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 ( T _ { X } , M _ { \text { gas } } , and Y _ { \mkern - 1.0 muX } ) based on a subsample of low- z relaxed clusters , and present a first measurement of the evolving L _ { X } - M _ { \text { tot } } relation ( with M _ { \text { tot } } estimated from Y _ { \mkern - 1.0 muX } ) obtained from a well-defined statistically complete cluster sample and with appropriate corrections for the Malmquist bias applied .
Finally , we present the derived cluster mass functions , estimate the systematic uncertainties in this measurement , and discuss the calculation of the likelihood function .
We confidently measure the evolution in the cluster comoving number density at a fixed mass threshold , e.g. , by a factor of 5.0 \pm 1.2 at M _ { 500 } = 2.5 \times 10 ^ { 14 } h ^ { -1 } M _ { \odot } between z = 0 and 0.5 .
This evolution reflects the growth of density perturbations and can be used for the cosmological constraints complementing those from the distance-redshift relation .