Abstract
We study the expected redshift evolution of galaxy cluster abundance
between 0 < z < 3 in different cosmologies, including the effects of
the cosmic equation of state parameter w=p/rho. Using the halo mass
function obtained in recent large scale numerical simulations, we
model the expected cluster yields in a 12 deg^2 SunyaevZeldovich
Effect (SZE) survey and a deep 10^4 deg^2 Xray survey over a wide
range of cosmological parameters. We quantify the statistical
differences among cosmologies using both the total number and redshift
distribution of clusters. Provided that the local cluster abundance is
known to a few percent accuracy, we find only mild degeneracies
between w and either Omega_m or h. As a result, both surveys will
provide improved constraints on Omega_m and w. The Omega_mw
degeneracy from both surveys is complementary to those found either in
studies of CMB anisotropies or of highredshift Supernovae (SNe). As a
result, combining these surveys together with either CMB or SNe
studies can reduce the statistical uncertainty on both w and Omega_m
to levels below what could be obtained by combining only the latter
two data sets. Our results indicate a formal statistical uncertainty
of about 3% (68% confidence) on both Omega_m and w when the SZE survey
is combined with either the CMB or SN data; the large number of
clusters in the Xray survey further suppresses the degeneracy between
w and both Omega_m and h. Systematics and internal evolution of
cluster structure at the present pose uncertainties above these
levels. We briefly discuss and quantify the relevant systematic
errors. By focusing on clusters with measured temperatures in the
Xray survey, we reduce our sensitivity to systematics such as
nonstandard evolution of internal cluster structure.
