  We study the ability of weak lensing surveys to detect galaxy clusters and
constrain cosmological parameters, in particular the equation of state of dark
energy. There are two major sources of noise for weak lensing cluster
measurements: the ``shape noise'' from the intrinsic ellipticities of galaxies;
and the large scale projection noise. We produce a filter for the shear field
which optimizes the signal-to-noise of shape-noise-dominated shear
measurements. Our Fisher-matrix analysis of this projected-mass observable
makes use of the shape of this mass function, and takes into account the
Poisson variance, sample variance, shape noise, and projected-mass noise, and
also the fact that the conversion of the shear signal into mass is
cosmology-dependent. The Fisher analysis is applied to both a nominal 15,000
square degree ground-based survey and a 1000 square degree space-based survey.
Assuming a detection threshold of S/N=5, we find both experiments detect
\~20,000 clusters, and yield 1-sigma constraints of ~0.07 for w0 and ~0.2 for
wa when combined with CMB data (for flat universe). The projection noise
exceeds the shape noise only for clusters at z<=0.1 and has little effect on
the derived dark-energy constraints. Sample variance does not significantly
affect either survey. Finally, we note that all these results are extremely
sensitive to the noise levels and detection thresholds that we impose. They can
be significantly improved if we combine ground and space surveys as independent
experiments and add their corresponding Fisher matrices.
