  The abundances of groups and clusters of galaxies are expected to have
changed substantially since high redshift, with the strength of this evolution
dependent upon fundamental cosmological parameters. Upcoming large redshift
surveys of distant galaxies will make it possible to measure these quantities
at z~1; when combined with the results of local redshift surveys currently
underway, the evolution of cluster abundances may be determined. The DEEP2
Redshift Survey, planned to begin in Spring 2002, is particularly well-suited
for this work because of the high spectroscopic resolution to be used; velocity
dispersions of groups will be readily measurable. In this paper, we determine
the constraints on dark energy models that counts of DEEP2 clusters should
provide. We find that comparing cosmological models using the simultaneous
distribution of clusters in both velocity dispersion and redshift yields
significantly stronger constraints than the redshift distribution alone. The
method can be made more powerful by employing a value of the fluctuation
amplitude sigma_8 determined with upcoming techniques (external to DEEP2) that
have no Omega_m degeneracy. The equation-of-state parameter for dark energy
models, w=P/rho, can then be measured to ~0.1 from observations of clusters
alone.
