A moderate investment of observing time with the International X-ray Observatory to study high-redshift galaxy clusters detected in future large-scale surveys, will provide cosmological measurements of fundamental importance. IXO observations, combin
ed with lensing follow-up, will measure the perturbation growth factor from z=0-2 with an accuracy comparable to, or possibly better than, that expected from observations of cosmic shear with JDEM, and redshift-space distortions with EUCLID. The growth of structure data derived from clusters will significantly improve our knowledge of the dark energy equation of state and will aid in constraining non-GR models for cosmic acceleration. IXO observations of the largest, dynamically relaxed clusters will provide a powerful, independent measurement of the cosmological expansion history using the apparent f_gas(z) trend. Systematic and statistical errors from this technique are competitive with SNIa and BAO studies, making the test extremely useful for improving the accuracy and reliability of the geometric cosmological measurements planned for LSST and JDEM. Only by employing a range of powerful, independent approaches, including those discussed here, can robust answers to puzzles as profound as the origin of cosmic acceleration be expected.
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 re
dshift leverage sufficiently large for the mass function evolution to be used as a useful growth of structure based dark energy probe. In this paper, we present cosmological parameter constraints obtained from Chandra observations of 36 clusters with <z>=0.55 derived from 400deg^2 ROSAT serendipitous survey and 49 brightest z=~0.05 clusters detected in the All-Sky Survey. Evolution of the mass function between these redshifts requires Omega_Lambda>0 with a ~5sigma significance, and constrains the dark energy equation of state parameter to w0=-1.14+-0.21, assuming constant w and flat universe. Cluster information also significantly improves constraints when combined with other methods. Fitting our cluster data jointly with the latest supernovae, WMAP, and baryonic acoustic oscillations measurements, we obtain w0=-0.991+-0.045 (stat) +-0.039 (sys), a factor of 1.5 reduction in statistical uncertainties, and nearly a factor of 2 improvement in systematics compared to constraints that can be obtained without clusters. The joint analysis of these four datasets puts a conservative upper limit on the masses of light neutrinos, Sum m_nu<0.33 eV at 95% CL. We also present updated measurements of Omega_M*h and sigma_8 from the low-redshift cluster mass function.
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 400deg^2 surveys. We provide a full reference for the data analysis proc
edures, present updated calibration of relations between the total cluster mass and its X-ray indicators (T_X, Mgas, and Y_X) based on a subsample of low-z relaxed clusters, and present a first measurement of the evolving L_X-Mtot relation (with Mtot estimated from Y_X) 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 +- 1.2 at M_500=2.5e14 h^-1 Msun 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.
